data.polynomial.erase_lead | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

fa256f00

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

69c6a5a1

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
 import Algebra.BigOperators.Fin
-import Data.Polynomial.Degree.Definitions
+import Algebra.Polynomial.Degree.Definitions
 
 #align_import data.polynomial.erase_lead from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"

69c6a5a1

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -118,7 +118,7 @@ theorem eraseLead_ne_zero (f0 : 2 ≤ f.support.card) : eraseLead f ≠ 0 :=
 #print Polynomial.lt_natDegree_of_mem_eraseLead_support /-
 theorem lt_natDegree_of_mem_eraseLead_support {a : ℕ} (h : a ∈ (eraseLead f).support) :
     a < f.natDegree := by
-  rw [erase_lead_support, mem_erase] at h 
+  rw [erase_lead_support, mem_erase] at h
   exact (le_nat_degree_of_mem_supp a h.2).lt_of_ne h.1
 #align polynomial.lt_nat_degree_of_mem_erase_lead_support Polynomial.lt_natDegree_of_mem_eraseLead_support
 -/

69c6a5a1

bump to nightly-2024-01-16-06

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

e3ed64a2

Diff

@@ -144,20 +144,18 @@ theorem eraseLead_support_card_lt (h : f ≠ 0) : (eraseLead f).support.card < f
 #align polynomial.erase_lead_support_card_lt Polynomial.eraseLead_support_card_lt
 -/
 
-#print Polynomial.eraseLead_card_support /-
 theorem eraseLead_card_support {c : ℕ} (fc : f.support.card = c) :
     f.eraseLead.support.card = c - 1 := by
   by_cases f0 : f = 0
   · rw [← fc, f0, erase_lead_zero, support_zero, card_empty]
   · rw [erase_lead_support, card_erase_of_mem (nat_degree_mem_support_of_nonzero f0), fc]
 #align polynomial.erase_lead_card_support Polynomial.eraseLead_card_support
--/
 
-#print Polynomial.eraseLead_card_support' /-
-theorem eraseLead_card_support' {c : ℕ} (fc : f.support.card = c + 1) :
+#print Polynomial.card_support_eraseLead' /-
+theorem card_support_eraseLead' {c : ℕ} (fc : f.support.card = c + 1) :
     f.eraseLead.support.card = c :=
   eraseLead_card_support fc
-#align polynomial.erase_lead_card_support' Polynomial.eraseLead_card_support'
+#align polynomial.erase_lead_card_support' Polynomial.card_support_eraseLead'
 -/
 
 #print Polynomial.eraseLead_monomial /-

69c6a5a1

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 -/
-import Mathbin.Algebra.BigOperators.Fin
-import Mathbin.Data.Polynomial.Degree.Definitions
+import Algebra.BigOperators.Fin
+import Data.Polynomial.Degree.Definitions
 
 #align_import data.polynomial.erase_lead from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"

69c6a5a1

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
-
-! This file was ported from Lean 3 source module data.polynomial.erase_lead
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.BigOperators.Fin
 import Mathbin.Data.Polynomial.Degree.Definitions
 
+#align_import data.polynomial.erase_lead from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
 /-!
 # Erase the leading term of a univariate polynomial

69c6a5a1

bump to nightly-2023-07-16-17

mathlib commit https://github.com/leanprover-community/mathlib/commit/2fe465deb81bcd7ccafa065bb686888a82f15372

6db63fa6

Diff

@@ -396,14 +396,13 @@ theorem card_support_eq {n : ℕ} :
     · intro i j hij
       have hi : i ∈ Set.range (Fin.castSuccEmb : Fin n ↪o Fin (n + 1)) :=
         by
-        rw [Fin.range_castSuccEmb, Set.mem_def]
+        rw [Fin.range_castSucc, Set.mem_def]
         exact lt_of_lt_of_le hij (nat.lt_succ_iff.mp j.2)
       obtain ⟨i, rfl⟩ := hi
       rw [fin.cast_succ.injective.extend_apply]
       by_cases hj : ∃ j₀, Fin.castSuccEmb j₀ = j
       · obtain ⟨j, rfl⟩ := hj
-        rwa [fin.cast_succ.injective.extend_apply, hk.lt_iff_lt, ←
-          Fin.castSuccEmb_lt_castSuccEmb_iff]
+        rwa [fin.cast_succ.injective.extend_apply, hk.lt_iff_lt, ← Fin.castSucc_lt_castSucc_iff]
       · rw [Function.extend_apply' _ _ _ hj]
         apply lt_nat_degree_of_mem_erase_lead_support
         rw [mem_support_iff, hf, finset_sum_coeff]
@@ -419,7 +418,7 @@ theorem card_support_eq {n : ℕ} :
         exact hx i
       · rw [Function.extend_apply' _ _ _ hi, Ne, leading_coeff_eq_zero, ← card_support_eq_zero, h]
         exact n.succ_ne_zero
-    · rw [Fin.sum_univ_castSuccEmb]
+    · rw [Fin.sum_univ_castSucc]
       simp only [fin.cast_succ.injective.extend_apply]
       rw [← hf, Function.extend_apply', Function.extend_apply', erase_lead_add_C_mul_X_pow]
       all_goals exact H
@@ -447,7 +446,7 @@ theorem card_support_eq_two :
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h
     refine' ⟨k 0, k 1, hk Nat.zero_lt_one, x 0, x 1, hx 0, hx 1, _⟩
-    rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_one]
+    rw [Fin.sum_univ_castSucc, Fin.sum_univ_one]
     rfl
   · rintro ⟨k, m, hkm, x, y, hx, hy, rfl⟩
     exact card_support_binomial hkm.ne hx hy
@@ -465,7 +464,7 @@ theorem card_support_eq_three :
     refine'
       ⟨k 0, k 1, k 2, hk Nat.zero_lt_one, hk (Nat.lt_succ_self 1), x 0, x 1, x 2, hx 0, hx 1, hx 2,
         _⟩
-    rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_castSuccEmb, Fin.sum_univ_one]
+    rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc, Fin.sum_univ_one]
     rfl
   · rintro ⟨k, m, n, hkm, hmn, x, y, z, hx, hy, hz, rfl⟩
     exact card_support_trinomial hkm hmn hx hy hz

69c6a5a1

bump to nightly-2023-07-06-11

mathlib commit https://github.com/leanprover-community/mathlib/commit/5dc6092d09e5e489106865241986f7f2ad28d4c8

a2f50eda

Diff

@@ -391,18 +391,19 @@ theorem card_support_eq {n : ℕ} :
       rintro ⟨i, hi⟩
       exact i.cast_succ_lt_last.Ne hi
     refine'
-      ⟨Function.extend Fin.castSucc k fun _ => f.nat_degree,
-        Function.extend Fin.castSucc x fun _ => f.leading_coeff, _, _, _⟩
+      ⟨Function.extend Fin.castSuccEmb k fun _ => f.nat_degree,
+        Function.extend Fin.castSuccEmb x fun _ => f.leading_coeff, _, _, _⟩
     · intro i j hij
-      have hi : i ∈ Set.range (Fin.castSucc : Fin n ↪o Fin (n + 1)) :=
+      have hi : i ∈ Set.range (Fin.castSuccEmb : Fin n ↪o Fin (n + 1)) :=
         by
-        rw [Fin.range_castSucc, Set.mem_def]
+        rw [Fin.range_castSuccEmb, Set.mem_def]
         exact lt_of_lt_of_le hij (nat.lt_succ_iff.mp j.2)
       obtain ⟨i, rfl⟩ := hi
       rw [fin.cast_succ.injective.extend_apply]
-      by_cases hj : ∃ j₀, Fin.castSucc j₀ = j
+      by_cases hj : ∃ j₀, Fin.castSuccEmb j₀ = j
       · obtain ⟨j, rfl⟩ := hj
-        rwa [fin.cast_succ.injective.extend_apply, hk.lt_iff_lt, ← Fin.castSucc_lt_castSucc_iff]
+        rwa [fin.cast_succ.injective.extend_apply, hk.lt_iff_lt, ←
+          Fin.castSuccEmb_lt_castSuccEmb_iff]
       · rw [Function.extend_apply' _ _ _ hj]
         apply lt_nat_degree_of_mem_erase_lead_support
         rw [mem_support_iff, hf, finset_sum_coeff]
@@ -412,13 +413,13 @@ theorem card_support_eq {n : ℕ} :
           rw [coeff_C_mul, coeff_X_pow, if_neg (hk.injective.ne hji.symm), MulZeroClass.mul_zero]
         · exact fun hi => (hi (mem_univ i)).elim
     · intro i
-      by_cases hi : ∃ i₀, Fin.castSucc i₀ = i
+      by_cases hi : ∃ i₀, Fin.castSuccEmb i₀ = i
       · obtain ⟨i, rfl⟩ := hi
         rw [fin.cast_succ.injective.extend_apply]
         exact hx i
       · rw [Function.extend_apply' _ _ _ hi, Ne, leading_coeff_eq_zero, ← card_support_eq_zero, h]
         exact n.succ_ne_zero
-    · rw [Fin.sum_univ_castSucc]
+    · rw [Fin.sum_univ_castSuccEmb]
       simp only [fin.cast_succ.injective.extend_apply]
       rw [← hf, Function.extend_apply', Function.extend_apply', erase_lead_add_C_mul_X_pow]
       all_goals exact H
@@ -446,7 +447,7 @@ theorem card_support_eq_two :
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h
     refine' ⟨k 0, k 1, hk Nat.zero_lt_one, x 0, x 1, hx 0, hx 1, _⟩
-    rw [Fin.sum_univ_castSucc, Fin.sum_univ_one]
+    rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_one]
     rfl
   · rintro ⟨k, m, hkm, x, y, hx, hy, rfl⟩
     exact card_support_binomial hkm.ne hx hy
@@ -464,7 +465,7 @@ theorem card_support_eq_three :
     refine'
       ⟨k 0, k 1, k 2, hk Nat.zero_lt_one, hk (Nat.lt_succ_self 1), x 0, x 1, x 2, hx 0, hx 1, hx 2,
         _⟩
-    rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc, Fin.sum_univ_one]
+    rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_castSuccEmb, Fin.sum_univ_one]
     rfl
   · rintro ⟨k, m, n, hkm, hmn, x, y, z, hx, hy, hz, rfl⟩
     exact card_support_trinomial hkm hmn hx hy hz

69c6a5a1

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -47,17 +47,23 @@ def eraseLead (f : R[X]) : R[X] :=
 
 section EraseLead
 
+#print Polynomial.eraseLead_support /-
 theorem eraseLead_support (f : R[X]) : f.eraseLead.support = f.support.eraseₓ f.natDegree := by
   simp only [erase_lead, support_erase]
 #align polynomial.erase_lead_support Polynomial.eraseLead_support
+-/
 
+#print Polynomial.eraseLead_coeff /-
 theorem eraseLead_coeff (i : ℕ) : f.eraseLead.coeff i = if i = f.natDegree then 0 else f.coeff i :=
   by simp only [erase_lead, coeff_erase]
 #align polynomial.erase_lead_coeff Polynomial.eraseLead_coeff
+-/
 
+#print Polynomial.eraseLead_coeff_natDegree /-
 @[simp]
 theorem eraseLead_coeff_natDegree : f.eraseLead.coeff f.natDegree = 0 := by simp [erase_lead_coeff]
 #align polynomial.erase_lead_coeff_nat_degree Polynomial.eraseLead_coeff_natDegree
+-/
 
 #print Polynomial.eraseLead_coeff_of_ne /-
 theorem eraseLead_coeff_of_ne (i : ℕ) (hi : i ≠ f.natDegree) : f.eraseLead.coeff i = f.coeff i := by
@@ -71,29 +77,37 @@ theorem eraseLead_zero : eraseLead (0 : R[X]) = 0 := by simp only [erase_lead, e
 #align polynomial.erase_lead_zero Polynomial.eraseLead_zero
 -/
 
+#print Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff /-
 @[simp]
 theorem eraseLead_add_monomial_natDegree_leadingCoeff (f : R[X]) :
     f.eraseLead + monomial f.natDegree f.leadingCoeff = f :=
   (add_comm _ _).trans (f.monomial_add_erase _)
 #align polynomial.erase_lead_add_monomial_nat_degree_leading_coeff Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff
+-/
 
+#print Polynomial.eraseLead_add_C_mul_X_pow /-
 @[simp]
 theorem eraseLead_add_C_mul_X_pow (f : R[X]) :
     f.eraseLead + C f.leadingCoeff * X ^ f.natDegree = f := by
   rw [C_mul_X_pow_eq_monomial, erase_lead_add_monomial_nat_degree_leading_coeff]
 #align polynomial.erase_lead_add_C_mul_X_pow Polynomial.eraseLead_add_C_mul_X_pow
+-/
 
+#print Polynomial.self_sub_monomial_natDegree_leadingCoeff /-
 @[simp]
 theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]) :
     f - monomial f.natDegree f.leadingCoeff = f.eraseLead :=
   (eq_sub_iff_add_eq.mpr (eraseLead_add_monomial_natDegree_leadingCoeff f)).symm
 #align polynomial.self_sub_monomial_nat_degree_leading_coeff Polynomial.self_sub_monomial_natDegree_leadingCoeff
+-/
 
+#print Polynomial.self_sub_C_mul_X_pow /-
 @[simp]
 theorem self_sub_C_mul_X_pow {R : Type _} [Ring R] (f : R[X]) :
     f - C f.leadingCoeff * X ^ f.natDegree = f.eraseLead := by
   rw [C_mul_X_pow_eq_monomial, self_sub_monomial_nat_degree_leading_coeff]
 #align polynomial.self_sub_C_mul_X_pow Polynomial.self_sub_C_mul_X_pow
+-/
 
 #print Polynomial.eraseLead_ne_zero /-
 theorem eraseLead_ne_zero (f0 : 2 ≤ f.support.card) : eraseLead f ≠ 0 :=
@@ -149,6 +163,7 @@ theorem eraseLead_card_support' {c : ℕ} (fc : f.support.card = c + 1) :
 #align polynomial.erase_lead_card_support' Polynomial.eraseLead_card_support'
 -/
 
+#print Polynomial.eraseLead_monomial /-
 @[simp]
 theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
   by
@@ -156,11 +171,14 @@ theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
   · subst r; simp only [monomial_zero_right, erase_lead_zero]
   · rw [erase_lead, nat_degree_monomial, if_neg hr, erase_monomial]
 #align polynomial.erase_lead_monomial Polynomial.eraseLead_monomial
+-/
 
+#print Polynomial.eraseLead_C /-
 @[simp]
 theorem eraseLead_C (r : R) : eraseLead (C r) = 0 :=
   eraseLead_monomial _ _
 #align polynomial.erase_lead_C Polynomial.eraseLead_C
+-/
 
 #print Polynomial.eraseLead_X /-
 @[simp]
@@ -176,10 +194,12 @@ theorem eraseLead_X_pow (n : ℕ) : eraseLead (X ^ n : R[X]) = 0 := by
 #align polynomial.erase_lead_X_pow Polynomial.eraseLead_X_pow
 -/
 
+#print Polynomial.eraseLead_C_mul_X_pow /-
 @[simp]
 theorem eraseLead_C_mul_X_pow (r : R) (n : ℕ) : eraseLead (C r * X ^ n) = 0 := by
   rw [C_mul_X_pow_eq_monomial, erase_lead_monomial]
 #align polynomial.erase_lead_C_mul_X_pow Polynomial.eraseLead_C_mul_X_pow
+-/
 
 #print Polynomial.eraseLead_add_of_natDegree_lt_left /-
 theorem eraseLead_add_of_natDegree_lt_left {p q : R[X]} (pq : q.natDegree < p.natDegree) :
@@ -251,6 +271,7 @@ theorem eraseLead_natDegree_le (f : R[X]) : (eraseLead f).natDegree ≤ f.natDeg
 
 end EraseLead
 
+#print Polynomial.induction_with_natDegree_le /-
 /-- An induction lemma for polynomials. It takes a natural number `N` as a parameter, that is
 required to be at least as big as the `nat_degree` of the polynomial.  This is useful to prove
 results where you want to change each term in a polynomial to something else depending on the
@@ -286,7 +307,9 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
       rw [Ne.def, leading_coeff_eq_zero, ← card_support_eq_zero, f0]
       exact Nat.succ_ne_zero _
 #align polynomial.induction_with_nat_degree_le Polynomial.induction_with_natDegree_le
+-/
 
+#print Polynomial.mono_map_natDegree_eq /-
 /-- Let `φ : R[x] → S[x]` be an additive map, `k : ℕ` a bound, and `fu : ℕ → ℕ` a
 "sufficiently monotone" map.  Assume also that
 * `φ` maps to `0` all monomials of degree less than `k`,
@@ -311,7 +334,9 @@ theorem mono_map_natDegree_eq {S F : Type _} [Semiring S] [AddMonoidHomClass F R
       · exact (FG (Nat.zero_le _)).elim
       · rwa [φ_k (not_le.mp FG), zero_add]
 #align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eq
+-/
 
+#print Polynomial.map_natDegree_eq_sub /-
 theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} {k : ℕ} (φ_k : ∀ f : R[X], f.natDegree < k → φ f = 0)
     (φ_mon : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n - k) :
@@ -319,16 +344,20 @@ theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[
   mono_map_natDegree_eq k (fun j => j - k) (by simp) (fun m n h => (tsub_lt_tsub_iff_right h).mpr)
     φ_k φ_mon
 #align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_sub
+-/
 
+#print Polynomial.map_natDegree_eq_natDegree /-
 theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]]
     {φ : F} (p) (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n) :
     (φ p).natDegree = p.natDegree :=
   (map_natDegree_eq_sub (fun f h => (Nat.not_lt_zero _ h).elim) (by simpa)).trans
     p.natDegree.sub_zero
 #align polynomial.map_nat_degree_eq_nat_degree Polynomial.map_natDegree_eq_natDegree
+-/
 
 open scoped BigOperators
 
+#print Polynomial.card_support_eq' /-
 theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : Function.Injective k)
     (hx : ∀ i, x i ≠ 0) : (∑ i, C (x i) * X ^ k i).support.card = n :=
   by
@@ -344,7 +373,9 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
     · exact hx j
     · exact fun m hm hmj => if_neg fun h => hmj.symm (hk h)
 #align polynomial.card_support_eq' Polynomial.card_support_eq'
+-/
 
+#print Polynomial.card_support_eq /-
 theorem card_support_eq {n : ℕ} :
     f.support.card = n ↔
       ∃ (k : Fin n → ℕ) (x : Fin n → R) (hk : StrictMono k) (hx : ∀ i, x i ≠ 0),
@@ -392,7 +423,9 @@ theorem card_support_eq {n : ℕ} :
       rw [← hf, Function.extend_apply', Function.extend_apply', erase_lead_add_C_mul_X_pow]
       all_goals exact H
 #align polynomial.card_support_eq Polynomial.card_support_eq
+-/
 
+#print Polynomial.card_support_eq_one /-
 theorem card_support_eq_one :
     f.support.card = 1 ↔ ∃ (k : ℕ) (x : R) (hx : x ≠ 0), f = C x * X ^ k :=
   by
@@ -402,7 +435,9 @@ theorem card_support_eq_one :
   · rintro ⟨k, x, hx, rfl⟩
     rw [support_C_mul_X_pow k hx, card_singleton]
 #align polynomial.card_support_eq_one Polynomial.card_support_eq_one
+-/
 
+#print Polynomial.card_support_eq_two /-
 theorem card_support_eq_two :
     f.support.card = 2 ↔
       ∃ (k m : ℕ) (hkm : k < m) (x y : R) (hx : x ≠ 0) (hy : y ≠ 0),
@@ -416,7 +451,9 @@ theorem card_support_eq_two :
   · rintro ⟨k, m, hkm, x, y, hx, hy, rfl⟩
     exact card_support_binomial hkm.ne hx hy
 #align polynomial.card_support_eq_two Polynomial.card_support_eq_two
+-/
 
+#print Polynomial.card_support_eq_three /-
 theorem card_support_eq_three :
     f.support.card = 3 ↔
       ∃ (k m n : ℕ) (hkm : k < m) (hmn : m < n) (x y z : R) (hx : x ≠ 0) (hy : y ≠ 0) (hz : z ≠ 0),
@@ -432,6 +469,7 @@ theorem card_support_eq_three :
   · rintro ⟨k, m, n, hkm, hmn, x, y, z, hx, hy, hz, rfl⟩
     exact card_support_trinomial hkm hmn hx hy hz
 #align polynomial.card_support_eq_three Polynomial.card_support_eq_three
+-/
 
 end Polynomial

69c6a5a1

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -107,7 +107,7 @@ theorem eraseLead_ne_zero (f0 : 2 ≤ f.support.card) : eraseLead f ≠ 0 :=
 #print Polynomial.lt_natDegree_of_mem_eraseLead_support /-
 theorem lt_natDegree_of_mem_eraseLead_support {a : ℕ} (h : a ∈ (eraseLead f).support) :
     a < f.natDegree := by
-  rw [erase_lead_support, mem_erase] at h
+  rw [erase_lead_support, mem_erase] at h 
   exact (le_nat_degree_of_mem_supp a h.2).lt_of_ne h.1
 #align polynomial.lt_nat_degree_of_mem_erase_lead_support Polynomial.lt_natDegree_of_mem_eraseLead_support
 -/
@@ -347,7 +347,7 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
 
 theorem card_support_eq {n : ℕ} :
     f.support.card = n ↔
-      ∃ (k : Fin n → ℕ)(x : Fin n → R)(hk : StrictMono k)(hx : ∀ i, x i ≠ 0),
+      ∃ (k : Fin n → ℕ) (x : Fin n → R) (hk : StrictMono k) (hx : ∀ i, x i ≠ 0),
         f = ∑ i, C (x i) * X ^ k i :=
   by
   refine' ⟨_, fun ⟨k, x, hk, hx, hf⟩ => hf.symm ▸ card_support_eq' k x hk.Injective hx⟩
@@ -393,7 +393,8 @@ theorem card_support_eq {n : ℕ} :
       all_goals exact H
 #align polynomial.card_support_eq Polynomial.card_support_eq
 
-theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x ≠ 0), f = C x * X ^ k :=
+theorem card_support_eq_one :
+    f.support.card = 1 ↔ ∃ (k : ℕ) (x : R) (hx : x ≠ 0), f = C x * X ^ k :=
   by
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h
@@ -404,7 +405,8 @@ theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x
 
 theorem card_support_eq_two :
     f.support.card = 2 ↔
-      ∃ (k m : ℕ)(hkm : k < m)(x y : R)(hx : x ≠ 0)(hy : y ≠ 0), f = C x * X ^ k + C y * X ^ m :=
+      ∃ (k m : ℕ) (hkm : k < m) (x y : R) (hx : x ≠ 0) (hy : y ≠ 0),
+        f = C x * X ^ k + C y * X ^ m :=
   by
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h
@@ -417,7 +419,7 @@ theorem card_support_eq_two :
 
 theorem card_support_eq_three :
     f.support.card = 3 ↔
-      ∃ (k m n : ℕ)(hkm : k < m)(hmn : m < n)(x y z : R)(hx : x ≠ 0)(hy : y ≠ 0)(hz : z ≠ 0),
+      ∃ (k m n : ℕ) (hkm : k < m) (hmn : m < n) (x y z : R) (hx : x ≠ 0) (hy : y ≠ 0) (hz : z ≠ 0),
         f = C x * X ^ k + C y * X ^ m + C z * X ^ n :=
   by
   refine' ⟨fun h => _, _⟩

69c6a5a1

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -29,7 +29,7 @@ and thus works for polynomials over semirings as well as rings.
 
 noncomputable section
 
-open Classical Polynomial
+open scoped Classical Polynomial
 
 open Polynomial Finset
 
@@ -207,9 +207,11 @@ theorem eraseLead_add_of_natDegree_lt_right {p q : R[X]} (pq : p.natDegree < q.n
 #align polynomial.erase_lead_add_of_nat_degree_lt_right Polynomial.eraseLead_add_of_natDegree_lt_right
 -/
 
+#print Polynomial.eraseLead_degree_le /-
 theorem eraseLead_degree_le : (eraseLead f).degree ≤ f.degree :=
   f.degree_erase_le _
 #align polynomial.erase_lead_degree_le Polynomial.eraseLead_degree_le
+-/
 
 #print Polynomial.eraseLead_natDegree_le_aux /-
 theorem eraseLead_natDegree_le_aux : (eraseLead f).natDegree ≤ f.natDegree :=
@@ -325,7 +327,7 @@ theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClas
     p.natDegree.sub_zero
 #align polynomial.map_nat_degree_eq_nat_degree Polynomial.map_natDegree_eq_natDegree
 
-open BigOperators
+open scoped BigOperators
 
 theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : Function.Injective k)
     (hx : ∀ i, x i ≠ 0) : (∑ i, C (x i) * X ^ k i).support.card = n :=

69c6a5a1

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -47,32 +47,14 @@ def eraseLead (f : R[X]) : R[X] :=
 
 section EraseLead
 
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 theorem eraseLead_support (f : R[X]) : f.eraseLead.support = f.support.eraseₓ f.natDegree := by
   simp only [erase_lead, support_erase]
 #align polynomial.erase_lead_support Polynomial.eraseLead_support
 
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 theorem eraseLead_coeff (i : ℕ) : f.eraseLead.coeff i = if i = f.natDegree then 0 else f.coeff i :=
   by simp only [erase_lead, coeff_erase]
 #align polynomial.erase_lead_coeff Polynomial.eraseLead_coeff
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_coeff_nat_degree Polynomial.eraseLead_coeff_natDegreeₓ'. -/
 @[simp]
 theorem eraseLead_coeff_natDegree : f.eraseLead.coeff f.natDegree = 0 := by simp [erase_lead_coeff]
 #align polynomial.erase_lead_coeff_nat_degree Polynomial.eraseLead_coeff_natDegree
@@ -89,48 +71,24 @@ theorem eraseLead_zero : eraseLead (0 : R[X]) = 0 := by simp only [erase_lead, e
 #align polynomial.erase_lead_zero Polynomial.eraseLead_zero
 -/
 
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 @[simp]
 theorem eraseLead_add_monomial_natDegree_leadingCoeff (f : R[X]) :
     f.eraseLead + monomial f.natDegree f.leadingCoeff = f :=
   (add_comm _ _).trans (f.monomial_add_erase _)
 #align polynomial.erase_lead_add_monomial_nat_degree_leading_coeff Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff
 
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 @[simp]
 theorem eraseLead_add_C_mul_X_pow (f : R[X]) :
     f.eraseLead + C f.leadingCoeff * X ^ f.natDegree = f := by
   rw [C_mul_X_pow_eq_monomial, erase_lead_add_monomial_nat_degree_leading_coeff]
 #align polynomial.erase_lead_add_C_mul_X_pow Polynomial.eraseLead_add_C_mul_X_pow
 
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 @[simp]
 theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]) :
     f - monomial f.natDegree f.leadingCoeff = f.eraseLead :=
   (eq_sub_iff_add_eq.mpr (eraseLead_add_monomial_natDegree_leadingCoeff f)).symm
 #align polynomial.self_sub_monomial_nat_degree_leading_coeff Polynomial.self_sub_monomial_natDegree_leadingCoeff
 
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 @[simp]
 theorem self_sub_C_mul_X_pow {R : Type _} [Ring R] (f : R[X]) :
     f - C f.leadingCoeff * X ^ f.natDegree = f.eraseLead := by
@@ -191,12 +149,6 @@ theorem eraseLead_card_support' {c : ℕ} (fc : f.support.card = c + 1) :
 #align polynomial.erase_lead_card_support' Polynomial.eraseLead_card_support'
 -/
 
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 @[simp]
 theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
   by
@@ -205,12 +157,6 @@ theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
   · rw [erase_lead, nat_degree_monomial, if_neg hr, erase_monomial]
 #align polynomial.erase_lead_monomial Polynomial.eraseLead_monomial
 
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 @[simp]
 theorem eraseLead_C (r : R) : eraseLead (C r) = 0 :=
   eraseLead_monomial _ _
@@ -230,12 +176,6 @@ theorem eraseLead_X_pow (n : ℕ) : eraseLead (X ^ n : R[X]) = 0 := by
 #align polynomial.erase_lead_X_pow Polynomial.eraseLead_X_pow
 -/
 
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 @[simp]
 theorem eraseLead_C_mul_X_pow (r : R) (n : ℕ) : eraseLead (C r * X ^ n) = 0 := by
   rw [C_mul_X_pow_eq_monomial, erase_lead_monomial]
@@ -267,12 +207,6 @@ theorem eraseLead_add_of_natDegree_lt_right {p q : R[X]} (pq : p.natDegree < q.n
 #align polynomial.erase_lead_add_of_nat_degree_lt_right Polynomial.eraseLead_add_of_natDegree_lt_right
 -/
 
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 theorem eraseLead_degree_le : (eraseLead f).degree ≤ f.degree :=
   f.degree_erase_le _
 #align polynomial.erase_lead_degree_le Polynomial.eraseLead_degree_le
@@ -315,12 +249,6 @@ theorem eraseLead_natDegree_le (f : R[X]) : (eraseLead f).natDegree ≤ f.natDeg
 
 end EraseLead
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.induction_with_nat_degree_le Polynomial.induction_with_natDegree_leₓ'. -/
 /-- An induction lemma for polynomials. It takes a natural number `N` as a parameter, that is
 required to be at least as big as the `nat_degree` of the polynomial.  This is useful to prove
 results where you want to change each term in a polynomial to something else depending on the
@@ -357,9 +285,6 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
       exact Nat.succ_ne_zero _
 #align polynomial.induction_with_nat_degree_le Polynomial.induction_with_natDegree_le
 
-/- warning: polynomial.mono_map_nat_degree_eq -> Polynomial.mono_map_natDegree_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eqₓ'. -/
 /-- Let `φ : R[x] → S[x]` be an additive map, `k : ℕ` a bound, and `fu : ℕ → ℕ` a
 "sufficiently monotone" map.  Assume also that
 * `φ` maps to `0` all monomials of degree less than `k`,
@@ -385,9 +310,6 @@ theorem mono_map_natDegree_eq {S F : Type _} [Semiring S] [AddMonoidHomClass F R
       · rwa [φ_k (not_le.mp FG), zero_add]
 #align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eq
 
-/- warning: polynomial.map_nat_degree_eq_sub -> Polynomial.map_natDegree_eq_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_subₓ'. -/
 theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} {k : ℕ} (φ_k : ∀ f : R[X], f.natDegree < k → φ f = 0)
     (φ_mon : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n - k) :
@@ -396,9 +318,6 @@ theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[
     φ_k φ_mon
 #align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_sub
 
-/- warning: polynomial.map_nat_degree_eq_nat_degree -> Polynomial.map_natDegree_eq_natDegree is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_nat_degree Polynomial.map_natDegree_eq_natDegreeₓ'. -/
 theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]]
     {φ : F} (p) (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n) :
     (φ p).natDegree = p.natDegree :=
@@ -408,9 +327,6 @@ theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClas
 
 open BigOperators
 
-/- warning: polynomial.card_support_eq' -> Polynomial.card_support_eq' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq' Polynomial.card_support_eq'ₓ'. -/
 theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : Function.Injective k)
     (hx : ∀ i, x i ≠ 0) : (∑ i, C (x i) * X ^ k i).support.card = n :=
   by
@@ -427,9 +343,6 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
     · exact fun m hm hmj => if_neg fun h => hmj.symm (hk h)
 #align polynomial.card_support_eq' Polynomial.card_support_eq'
 
-/- warning: polynomial.card_support_eq -> Polynomial.card_support_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq Polynomial.card_support_eqₓ'. -/
 theorem card_support_eq {n : ℕ} :
     f.support.card = n ↔
       ∃ (k : Fin n → ℕ)(x : Fin n → R)(hk : StrictMono k)(hx : ∀ i, x i ≠ 0),
@@ -478,12 +391,6 @@ theorem card_support_eq {n : ℕ} :
       all_goals exact H
 #align polynomial.card_support_eq Polynomial.card_support_eq
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_one Polynomial.card_support_eq_oneₓ'. -/
 theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x ≠ 0), f = C x * X ^ k :=
   by
   refine' ⟨fun h => _, _⟩
@@ -493,9 +400,6 @@ theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x
     rw [support_C_mul_X_pow k hx, card_singleton]
 #align polynomial.card_support_eq_one Polynomial.card_support_eq_one
 
-/- warning: polynomial.card_support_eq_two -> Polynomial.card_support_eq_two is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_two Polynomial.card_support_eq_twoₓ'. -/
 theorem card_support_eq_two :
     f.support.card = 2 ↔
       ∃ (k m : ℕ)(hkm : k < m)(x y : R)(hx : x ≠ 0)(hy : y ≠ 0), f = C x * X ^ k + C y * X ^ m :=
@@ -509,9 +413,6 @@ theorem card_support_eq_two :
     exact card_support_binomial hkm.ne hx hy
 #align polynomial.card_support_eq_two Polynomial.card_support_eq_two
 
-/- warning: polynomial.card_support_eq_three -> Polynomial.card_support_eq_three is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_three Polynomial.card_support_eq_threeₓ'. -/
 theorem card_support_eq_three :
     f.support.card = 3 ↔
       ∃ (k m n : ℕ)(hkm : k < m)(hmn : m < n)(x y z : R)(hx : x ≠ 0)(hy : y ≠ 0)(hz : z ≠ 0),

69c6a5a1

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -201,8 +201,7 @@ Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_
 theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
   by
   by_cases hr : r = 0
-  · subst r
-    simp only [monomial_zero_right, erase_lead_zero]
+  · subst r; simp only [monomial_zero_right, erase_lead_zero]
   · rw [erase_lead, nat_degree_monomial, if_neg hr, erase_monomial]
 #align polynomial.erase_lead_monomial Polynomial.eraseLead_monomial

69c6a5a1

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -359,10 +359,7 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
 #align polynomial.induction_with_nat_degree_le Polynomial.induction_with_natDegree_le
 
 /- warning: polynomial.mono_map_nat_degree_eq -> Polynomial.mono_map_natDegree_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eqₓ'. -/
 /-- Let `φ : R[x] → S[x]` be an additive map, `k : ℕ` a bound, and `fu : ℕ → ℕ` a
 "sufficiently monotone" map.  Assume also that
@@ -390,10 +387,7 @@ theorem mono_map_natDegree_eq {S F : Type _} [Semiring S] [AddMonoidHomClass F R
 #align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eq
 
 /- warning: polynomial.map_nat_degree_eq_sub -> Polynomial.map_natDegree_eq_sub is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_subₓ'. -/
 theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} {k : ℕ} (φ_k : ∀ f : R[X], f.natDegree < k → φ f = 0)
@@ -404,10 +398,7 @@ theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[
 #align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_sub
 
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(Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_nat_degree Polynomial.map_natDegree_eq_natDegreeₓ'. -/
 theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]]
     {φ : F} (p) (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n) :
@@ -419,10 +410,7 @@ theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClas
 open BigOperators
 
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 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq' Polynomial.card_support_eq'ₓ'. -/
 theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : Function.Injective k)
     (hx : ∀ i, x i ≠ 0) : (∑ i, C (x i) * X ^ k i).support.card = n :=
@@ -441,10 +429,7 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
 #align polynomial.card_support_eq' Polynomial.card_support_eq'
 
 /- warning: polynomial.card_support_eq -> Polynomial.card_support_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq Polynomial.card_support_eqₓ'. -/
 theorem card_support_eq {n : ℕ} :
     f.support.card = n ↔
@@ -510,10 +495,7 @@ theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x
 #align polynomial.card_support_eq_one Polynomial.card_support_eq_one
 
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 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_two Polynomial.card_support_eq_twoₓ'. -/
 theorem card_support_eq_two :
     f.support.card = 2 ↔
@@ -529,10 +511,7 @@ theorem card_support_eq_two :
 #align polynomial.card_support_eq_two Polynomial.card_support_eq_two
 
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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) z) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) z) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) z) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) z) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))))))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_three Polynomial.card_support_eq_threeₓ'. -/
 theorem card_support_eq_three :
     f.support.card = 3 ↔

69c6a5a1

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -93,7 +93,7 @@ theorem eraseLead_zero : eraseLead (0 : R[X]) = 0 := by simp only [erase_lead, e
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Polynomial.natDegree.{u1} R _inst_1 f)) (Polynomial.leadingCoeff.{u1} R _inst_1 f))) f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Polynomial.natDegree.{u1} R _inst_1 f)) (Polynomial.leadingCoeff.{u1} R _inst_1 f))) f
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Polynomial.natDegree.{u1} R _inst_1 f)) (Polynomial.leadingCoeff.{u1} R _inst_1 f))) f
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_add_monomial_nat_degree_leading_coeff Polynomial.eraseLead_add_monomial_natDegree_leadingCoeffₓ'. -/
 @[simp]
 theorem eraseLead_add_monomial_natDegree_leadingCoeff (f : R[X]) :
@@ -117,7 +117,7 @@ theorem eraseLead_add_C_mul_X_pow (f : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R _inst_2) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R _inst_2) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
+  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R _inst_2) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.self_sub_monomial_nat_degree_leading_coeff Polynomial.self_sub_monomial_natDegree_leadingCoeffₓ'. -/
 @[simp]
 theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]) :
@@ -195,7 +195,7 @@ theorem eraseLead_card_support' {c : ℕ} (fc : f.support.card = c + 1) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (i : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 i) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (i : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 i) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (i : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 i) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_monomial Polynomial.eraseLead_monomialₓ'. -/
 @[simp]
 theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
@@ -362,7 +362,7 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} {F : Type.{u3}} [_inst_2 : Semiring.{u2} S] [_inst_3 : AddMonoidHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} (k : Nat) (fu : Nat -> Nat), (forall {n : Nat}, (LE.le.{0} Nat Nat.hasLe n k) -> (Eq.{1} Nat (fu n) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) -> (forall {n : Nat} {m : Nat}, (LE.le.{0} Nat Nat.hasLe k n) -> (LT.lt.{0} Nat Nat.hasLt n m) -> (LT.lt.{0} Nat Nat.hasLt (fu n) (fu m))) -> (forall {f : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ f) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} (k : Nat) (fu : Nat -> Nat), (forall {n : Nat}, (LE.le.{0} Nat instLENat n k) -> (Eq.{1} Nat (fu n) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (forall {n : Nat} {m : Nat}, (LE.le.{0} Nat instLENat k n) -> (LT.lt.{0} Nat instLTNat n m) -> (LT.lt.{0} Nat instLTNat (fu n) (fu m))) -> (forall {f : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} (k : Nat) (fu : Nat -> Nat), (forall {n : Nat}, (LE.le.{0} Nat instLENat n k) -> (Eq.{1} Nat (fu n) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (forall {n : Nat} {m : Nat}, (LE.le.{0} Nat instLENat k n) -> (LT.lt.{0} Nat instLTNat n m) -> (LT.lt.{0} Nat instLTNat (fu n) (fu m))) -> (forall {f : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eqₓ'. -/
 /-- Let `φ : R[x] → S[x]` be an additive map, `k : ℕ` a bound, and `fu : ℕ → ℕ` a
 "sufficiently monotone" map.  Assume also that
@@ -393,7 +393,7 @@ theorem mono_map_natDegree_eq {S F : Type _} [Semiring S] [AddMonoidHomClass F R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} {F : Type.{u3}} [_inst_2 : Semiring.{u2} S] [_inst_3 : AddMonoidHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ f) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n k))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R _inst_1 p) k))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n k))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) k))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n k))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) k))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_subₓ'. -/
 theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} {k : ℕ} (φ_k : ∀ f : R[X], f.natDegree < k → φ f = 0)
@@ -407,7 +407,7 @@ theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} {F : Type.{u3}} [_inst_2 : Semiring.{u2} S] [_inst_3 : AddMonoidHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))] {φ : F} (p : Polynomial.{u1} R _inst_1), (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) n)) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} (p : Polynomial.{u1} R _inst_1), (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) n)) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} (p : Polynomial.{u1} R _inst_1), (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) n)) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_nat_degree Polynomial.map_natDegree_eq_natDegreeₓ'. -/
 theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]]
     {φ : F} (p) (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n) :

69c6a5a1

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -105,7 +105,7 @@ theorem eraseLead_add_monomial_natDegree_leadingCoeff (f : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 f)))) f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 f)))) f
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 f)))) f
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_add_C_mul_X_pow Polynomial.eraseLead_add_C_mul_X_powₓ'. -/
 @[simp]
 theorem eraseLead_add_C_mul_X_pow (f : R[X]) :
@@ -129,7 +129,7 @@ theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.ring.{u1} R _inst_2)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
+  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.self_sub_C_mul_X_pow Polynomial.self_sub_C_mul_X_powₓ'. -/
 @[simp]
 theorem self_sub_C_mul_X_pow {R : Type _} [Ring R] (f : R[X]) :
@@ -210,7 +210,7 @@ theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_C Polynomial.eraseLead_Cₓ'. -/
 @[simp]
 theorem eraseLead_C (r : R) : eraseLead (C r) = 0 :=
@@ -235,7 +235,7 @@ theorem eraseLead_X_pow (n : ℕ) : eraseLead (X ^ n : R[X]) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_C_mul_X_pow Polynomial.eraseLead_C_mul_X_powₓ'. -/
 @[simp]
 theorem eraseLead_C_mul_X_pow (r : R) (n : ℕ) : eraseLead (C r * X ^ n) = 0 := by
@@ -320,7 +320,7 @@ end EraseLead
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (P : (Polynomial.{u1} R _inst_1) -> Prop) (N : Nat), (P (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (forall (n : Nat) (r : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (LE.le.{0} Nat Nat.hasLe n N) -> (P (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))) -> (forall (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 g)) -> (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 g) N) -> (P f) -> (P g) -> (P (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) f g))) -> (forall (f : Polynomial.{u1} R _inst_1), (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 f) N) -> (P f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (P : (Polynomial.{u1} R _inst_1) -> Prop) (N : Nat), (P (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (n : Nat) (r : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (LE.le.{0} Nat instLENat n N) -> (P (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))) -> (forall (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 g)) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 g) N) -> (P f) -> (P g) -> (P (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) f g))) -> (forall (f : Polynomial.{u1} R _inst_1), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 f) N) -> (P f))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (P : (Polynomial.{u1} R _inst_1) -> Prop) (N : Nat), (P (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (n : Nat) (r : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (LE.le.{0} Nat instLENat n N) -> (P (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))) -> (forall (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 g)) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 g) N) -> (P f) -> (P g) -> (P (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) f g))) -> (forall (f : Polynomial.{u1} R _inst_1), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 f) N) -> (P f))
 Case conversion may be inaccurate. Consider using '#align polynomial.induction_with_nat_degree_le Polynomial.induction_with_natDegree_leₓ'. -/
 /-- An induction lemma for polynomials. It takes a natural number `N` as a parameter, that is
 required to be at least as big as the `nat_degree` of the polynomial.  This is useful to prove
@@ -422,7 +422,7 @@ open BigOperators
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq' Polynomial.card_support_eq'ₓ'. -/
 theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : Function.Injective k)
     (hx : ∀ i, x i ≠ 0) : (∑ i, C (x i) * X ^ k i).support.card = n :=
@@ -444,7 +444,7 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) n) (Exists.{1} ((Fin n) -> Nat) (fun (k : (Fin n) -> Nat) => Exists.{succ u1} ((Fin n) -> R) (fun (x : (Fin n) -> R) => Exists.{0} (StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.partialOrder n)) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k) (fun (hk : StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.partialOrder n)) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k) => Exists.{0} (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) n) (Exists.{1} ((Fin n) -> Nat) (fun (k : (Fin n) -> Nat) => Exists.{succ u1} ((Fin n) -> R) (fun (x : (Fin n) -> R) => Exists.{0} (StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) (fun (hk : StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) => Exists.{0} (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) n) (Exists.{1} ((Fin n) -> Nat) (fun (k : (Fin n) -> Nat) => Exists.{succ u1} ((Fin n) -> R) (fun (x : (Fin n) -> R) => Exists.{0} (StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) (fun (hk : StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) => Exists.{0} (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq Polynomial.card_support_eqₓ'. -/
 theorem card_support_eq {n : ℕ} :
     f.support.card = n ↔
@@ -498,7 +498,7 @@ theorem card_support_eq {n : ℕ} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Exists.{1} Nat (fun (k : Nat) => Exists.{succ u1} R (fun (x : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Exists.{1} Nat (fun (k : Nat) => Exists.{succ u1} R (fun (x : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Exists.{1} Nat (fun (k : Nat) => Exists.{succ u1} R (fun (x : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_one Polynomial.card_support_eq_oneₓ'. -/
 theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x ≠ 0), f = C x * X ^ k :=
   by
@@ -513,7 +513,7 @@ theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (LT.lt.{0} Nat Nat.hasLt k m) (fun (hkm : LT.lt.{0} Nat Nat.hasLt k m) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m)))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m)))))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m)))))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_two Polynomial.card_support_eq_twoₓ'. -/
 theorem card_support_eq_two :
     f.support.card = 2 ↔
@@ -532,7 +532,7 @@ theorem card_support_eq_two :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{1} Nat (fun (n : Nat) => Exists.{0} (LT.lt.{0} Nat Nat.hasLt k m) (fun (hkm : LT.lt.{0} Nat Nat.hasLt k m) => Exists.{0} (LT.lt.{0} Nat Nat.hasLt m n) (fun (hmn : LT.lt.{0} Nat Nat.hasLt m n) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{succ u1} R (fun (z : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Exists.{0} (Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hz : Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) z) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{1} Nat (fun (n : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{0} (LT.lt.{0} Nat instLTNat m n) (fun (hmn : LT.lt.{0} Nat instLTNat m n) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{succ u1} R (fun (z : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hz : Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) z) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R 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Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) z) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R 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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{1} Nat (fun (n : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{0} (LT.lt.{0} Nat instLTNat m n) (fun (hmn : LT.lt.{0} Nat instLTNat m n) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{succ u1} R (fun (z : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hz : Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) z) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R 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Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) z) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))))))))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_three Polynomial.card_support_eq_threeₓ'. -/
 theorem card_support_eq_three :
     f.support.card = 3 ↔

69c6a5a1

bump to nightly-2023-05-18-03

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

b46e9d53

Diff

@@ -93,7 +93,7 @@ theorem eraseLead_zero : eraseLead (0 : R[X]) = 0 := by simp only [erase_lead, e
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Polynomial.natDegree.{u1} R _inst_1 f)) (Polynomial.leadingCoeff.{u1} R _inst_1 f))) f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Polynomial.natDegree.{u1} R _inst_1 f)) (Polynomial.leadingCoeff.{u1} R _inst_1 f))) f
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Polynomial.natDegree.{u1} R _inst_1 f)) (Polynomial.leadingCoeff.{u1} R _inst_1 f))) f
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_add_monomial_nat_degree_leading_coeff Polynomial.eraseLead_add_monomial_natDegree_leadingCoeffₓ'. -/
 @[simp]
 theorem eraseLead_add_monomial_natDegree_leadingCoeff (f : R[X]) :
@@ -117,7 +117,7 @@ theorem eraseLead_add_C_mul_X_pow (f : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R _inst_2) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R _inst_2) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
+  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R _inst_2) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.self_sub_monomial_nat_degree_leading_coeff Polynomial.self_sub_monomial_natDegree_leadingCoeffₓ'. -/
 @[simp]
 theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]) :
@@ -195,7 +195,7 @@ theorem eraseLead_card_support' {c : ℕ} (fc : f.support.card = c + 1) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (i : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 i) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (i : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 i) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (i : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 i) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_monomial Polynomial.eraseLead_monomialₓ'. -/
 @[simp]
 theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
@@ -362,7 +362,7 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} {F : Type.{u3}} [_inst_2 : Semiring.{u2} S] [_inst_3 : AddMonoidHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} (k : Nat) (fu : Nat -> Nat), (forall {n : Nat}, (LE.le.{0} Nat Nat.hasLe n k) -> (Eq.{1} Nat (fu n) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) -> (forall {n : Nat} {m : Nat}, (LE.le.{0} Nat Nat.hasLe k n) -> (LT.lt.{0} Nat Nat.hasLt n m) -> (LT.lt.{0} Nat Nat.hasLt (fu n) (fu m))) -> (forall {f : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ f) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} (k : Nat) (fu : Nat -> Nat), (forall {n : Nat}, (LE.le.{0} Nat instLENat n k) -> (Eq.{1} Nat (fu n) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (forall {n : Nat} {m : Nat}, (LE.le.{0} Nat instLENat k n) -> (LT.lt.{0} Nat instLTNat n m) -> (LT.lt.{0} Nat instLTNat (fu n) (fu m))) -> (forall {f : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} (k : Nat) (fu : Nat -> Nat), (forall {n : Nat}, (LE.le.{0} Nat instLENat n k) -> (Eq.{1} Nat (fu n) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (forall {n : Nat} {m : Nat}, (LE.le.{0} Nat instLENat k n) -> (LT.lt.{0} Nat instLTNat n m) -> (LT.lt.{0} Nat instLTNat (fu n) (fu m))) -> (forall {f : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eqₓ'. -/
 /-- Let `φ : R[x] → S[x]` be an additive map, `k : ℕ` a bound, and `fu : ℕ → ℕ` a
 "sufficiently monotone" map.  Assume also that
@@ -393,7 +393,7 @@ theorem mono_map_natDegree_eq {S F : Type _} [Semiring S] [AddMonoidHomClass F R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} {F : Type.{u3}} [_inst_2 : Semiring.{u2} S] [_inst_3 : AddMonoidHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ f) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun 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(Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n k))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R _inst_1 p) k))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n k))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) k))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n k))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) k))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_subₓ'. -/
 theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} {k : ℕ} (φ_k : ∀ f : R[X], f.natDegree < k → φ f = 0)
@@ -407,7 +407,7 @@ theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} {F : Type.{u3}} [_inst_2 : Semiring.{u2} S] [_inst_3 : AddMonoidHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))] {φ : F} (p : Polynomial.{u1} R _inst_1), (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) n)) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} (p : Polynomial.{u1} R _inst_1), (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) n)) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} (p : Polynomial.{u1} R _inst_1), (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) n)) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_nat_degree Polynomial.map_natDegree_eq_natDegreeₓ'. -/
 theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]]
     {φ : F} (p) (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n) :

69c6a5a1

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -268,11 +268,15 @@ theorem eraseLead_add_of_natDegree_lt_right {p q : R[X]} (pq : p.natDegree < q.n
 #align polynomial.erase_lead_add_of_nat_degree_lt_right Polynomial.eraseLead_add_of_natDegree_lt_right
 -/
 
-#print Polynomial.eraseLead_degree_le /-
+/- warning: polynomial.erase_lead_degree_le -> Polynomial.eraseLead_degree_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} R _inst_1 (Polynomial.eraseLead.{u1} R _inst_1 f)) (Polynomial.degree.{u1} R _inst_1 f)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u1} R _inst_1 (Polynomial.eraseLead.{u1} R _inst_1 f)) (Polynomial.degree.{u1} R _inst_1 f)
+Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_degree_le Polynomial.eraseLead_degree_leₓ'. -/
 theorem eraseLead_degree_le : (eraseLead f).degree ≤ f.degree :=
   f.degree_erase_le _
 #align polynomial.erase_lead_degree_le Polynomial.eraseLead_degree_le
--/
 
 #print Polynomial.eraseLead_natDegree_le_aux /-
 theorem eraseLead_natDegree_le_aux : (eraseLead f).natDegree ≤ f.natDegree :=

69c6a5a1

bump to nightly-2023-03-14-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

d4b38a42

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
 
 ! This file was ported from Lean 3 source module data.polynomial.erase_lead
-! leanprover-community/mathlib commit fa256f00ce018e7b40e1dc756e403c86680bf448
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Data.Polynomial.Degree.Definitions
 /-!
 # Erase the leading term of a univariate polynomial
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Definition
 
 * `erase_lead f`: the polynomial `f - leading term of f`

fa256f00

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -90,7 +90,7 @@ theorem eraseLead_zero : eraseLead (0 : R[X]) = 0 := by simp only [erase_lead, e
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Polynomial.natDegree.{u1} R _inst_1 f)) (Polynomial.leadingCoeff.{u1} R _inst_1 f))) f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Polynomial.natDegree.{u1} R _inst_1 f)) (Polynomial.leadingCoeff.{u1} R _inst_1 f))) f
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 (Polynomial.natDegree.{u1} R _inst_1 f)) (Polynomial.leadingCoeff.{u1} R _inst_1 f))) f
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_add_monomial_nat_degree_leading_coeff Polynomial.eraseLead_add_monomial_natDegree_leadingCoeffₓ'. -/
 @[simp]
 theorem eraseLead_add_monomial_natDegree_leadingCoeff (f : R[X]) :
@@ -102,7 +102,7 @@ theorem eraseLead_add_monomial_natDegree_leadingCoeff (f : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 f)))) f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 f)))) f
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 f)))) f
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_add_C_mul_X_pow Polynomial.eraseLead_add_C_mul_X_powₓ'. -/
 @[simp]
 theorem eraseLead_add_C_mul_X_pow (f : R[X]) :
@@ -114,7 +114,7 @@ theorem eraseLead_add_C_mul_X_pow (f : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R _inst_2) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R _inst_2) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
+  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toSemiring.{u1} R _inst_2) (Ring.toSemiring.{u1} R _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R _inst_2) R (Ring.toSemiring.{u1} R _inst_2) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R _inst_2) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.self_sub_monomial_nat_degree_leading_coeff Polynomial.self_sub_monomial_natDegree_leadingCoeffₓ'. -/
 @[simp]
 theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]) :
@@ -126,7 +126,7 @@ theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.ring.{u1} R _inst_2)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
+  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.self_sub_C_mul_X_pow Polynomial.self_sub_C_mul_X_powₓ'. -/
 @[simp]
 theorem self_sub_C_mul_X_pow {R : Type _} [Ring R] (f : R[X]) :
@@ -192,7 +192,7 @@ theorem eraseLead_card_support' {c : ℕ} (fc : f.support.card = c + 1) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (i : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 i) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (i : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 i) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (i : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 i) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_monomial Polynomial.eraseLead_monomialₓ'. -/
 @[simp]
 theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
@@ -207,7 +207,7 @@ theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_C Polynomial.eraseLead_Cₓ'. -/
 @[simp]
 theorem eraseLead_C (r : R) : eraseLead (C r) = 0 :=
@@ -232,7 +232,7 @@ theorem eraseLead_X_pow (n : ℕ) : eraseLead (X ^ n : R[X]) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_C_mul_X_pow Polynomial.eraseLead_C_mul_X_powₓ'. -/
 @[simp]
 theorem eraseLead_C_mul_X_pow (r : R) (n : ℕ) : eraseLead (C r * X ^ n) = 0 := by
@@ -313,7 +313,7 @@ end EraseLead
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (P : (Polynomial.{u1} R _inst_1) -> Prop) (N : Nat), (P (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (forall (n : Nat) (r : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (LE.le.{0} Nat Nat.hasLe n N) -> (P (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))) -> (forall (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 g)) -> (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 g) N) -> (P f) -> (P g) -> (P (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) f g))) -> (forall (f : Polynomial.{u1} R _inst_1), (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 f) N) -> (P f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (P : (Polynomial.{u1} R _inst_1) -> Prop) (N : Nat), (P (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (n : Nat) (r : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (LE.le.{0} Nat instLENat n N) -> (P (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))) -> (forall (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 g)) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 g) N) -> (P f) -> (P g) -> (P (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) f g))) -> (forall (f : Polynomial.{u1} R _inst_1), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 f) N) -> (P f))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (P : (Polynomial.{u1} R _inst_1) -> Prop) (N : Nat), (P (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (n : Nat) (r : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (LE.le.{0} Nat instLENat n N) -> (P (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))) -> (forall (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 g)) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 g) N) -> (P f) -> (P g) -> (P (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) f g))) -> (forall (f : Polynomial.{u1} R _inst_1), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 f) N) -> (P f))
 Case conversion may be inaccurate. Consider using '#align polynomial.induction_with_nat_degree_le Polynomial.induction_with_natDegree_leₓ'. -/
 /-- An induction lemma for polynomials. It takes a natural number `N` as a parameter, that is
 required to be at least as big as the `nat_degree` of the polynomial.  This is useful to prove
@@ -355,7 +355,7 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} {F : Type.{u3}} [_inst_2 : Semiring.{u2} S] [_inst_3 : AddMonoidHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} (k : Nat) (fu : Nat -> Nat), (forall {n : Nat}, (LE.le.{0} Nat Nat.hasLe n k) -> (Eq.{1} Nat (fu n) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) -> (forall {n : Nat} {m : Nat}, (LE.le.{0} Nat Nat.hasLe k n) -> (LT.lt.{0} Nat Nat.hasLt n m) -> (LT.lt.{0} Nat Nat.hasLt (fu n) (fu m))) -> (forall {f : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ f) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} (k : Nat) (fu : Nat -> Nat), (forall {n : Nat}, (LE.le.{0} Nat instLENat n k) -> (Eq.{1} Nat (fu n) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (forall {n : Nat} {m : Nat}, (LE.le.{0} Nat instLENat k n) -> (LT.lt.{0} Nat instLTNat n m) -> (LT.lt.{0} Nat instLTNat (fu n) (fu m))) -> (forall {f : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} (k : Nat) (fu : Nat -> Nat), (forall {n : Nat}, (LE.le.{0} Nat instLENat n k) -> (Eq.{1} Nat (fu n) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (forall {n : Nat} {m : Nat}, (LE.le.{0} Nat instLENat k n) -> (LT.lt.{0} Nat instLTNat n m) -> (LT.lt.{0} Nat instLTNat (fu n) (fu m))) -> (forall {f : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
 Case conversion may be inaccurate. Consider using '#align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eqₓ'. -/
 /-- Let `φ : R[x] → S[x]` be an additive map, `k : ℕ` a bound, and `fu : ℕ → ℕ` a
 "sufficiently monotone" map.  Assume also that
@@ -386,7 +386,7 @@ theorem mono_map_natDegree_eq {S F : Type _} [Semiring S] [AddMonoidHomClass F R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} {F : Type.{u3}} [_inst_2 : Semiring.{u2} S] [_inst_3 : AddMonoidHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ f) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun 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(Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n k))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R _inst_1 p) k))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => 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(AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n k))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) k))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n k))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R _inst_1 p) k))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_subₓ'. -/
 theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} {k : ℕ} (φ_k : ∀ f : R[X], f.natDegree < k → φ f = 0)
@@ -400,7 +400,7 @@ theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} {F : Type.{u3}} [_inst_2 : Semiring.{u2} S] [_inst_3 : AddMonoidHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))] {φ : F} (p : Polynomial.{u1} R _inst_1), (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) n)) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} (p : Polynomial.{u1} R _inst_1), (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) n)) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} (p : Polynomial.{u1} R _inst_1), (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) n)) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_nat_degree Polynomial.map_natDegree_eq_natDegreeₓ'. -/
 theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]]
     {φ : F} (p) (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n) :
@@ -415,7 +415,7 @@ open BigOperators
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq' Polynomial.card_support_eq'ₓ'. -/
 theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : Function.Injective k)
     (hx : ∀ i, x i ≠ 0) : (∑ i, C (x i) * X ^ k i).support.card = n :=
@@ -437,7 +437,7 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) n) (Exists.{1} ((Fin n) -> Nat) (fun (k : (Fin n) -> Nat) => Exists.{succ u1} ((Fin n) -> R) (fun (x : (Fin n) -> R) => Exists.{0} (StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.partialOrder n)) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k) (fun (hk : StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.partialOrder n)) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k) => Exists.{0} (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) n) (Exists.{1} ((Fin n) -> Nat) (fun (k : (Fin n) -> Nat) => Exists.{succ u1} ((Fin n) -> R) (fun (x : (Fin n) -> R) => Exists.{0} (StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) (fun (hk : StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) => Exists.{0} (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) n) (Exists.{1} ((Fin n) -> Nat) (fun (k : (Fin n) -> Nat) => Exists.{succ u1} ((Fin n) -> R) (fun (x : (Fin n) -> R) => Exists.{0} (StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) (fun (hk : StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) => Exists.{0} (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq Polynomial.card_support_eqₓ'. -/
 theorem card_support_eq {n : ℕ} :
     f.support.card = n ↔
@@ -491,7 +491,7 @@ theorem card_support_eq {n : ℕ} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Exists.{1} Nat (fun (k : Nat) => Exists.{succ u1} R (fun (x : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Exists.{1} Nat (fun (k : Nat) => Exists.{succ u1} R (fun (x : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Exists.{1} Nat (fun (k : Nat) => Exists.{succ u1} R (fun (x : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_one Polynomial.card_support_eq_oneₓ'. -/
 theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x ≠ 0), f = C x * X ^ k :=
   by
@@ -506,7 +506,7 @@ theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (LT.lt.{0} Nat Nat.hasLt k m) (fun (hkm : LT.lt.{0} Nat Nat.hasLt k m) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m)))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m)))))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m)))))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_two Polynomial.card_support_eq_twoₓ'. -/
 theorem card_support_eq_two :
     f.support.card = 2 ↔
@@ -525,7 +525,7 @@ theorem card_support_eq_two :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{1} Nat (fun (n : Nat) => Exists.{0} (LT.lt.{0} Nat Nat.hasLt k m) (fun (hkm : LT.lt.{0} Nat Nat.hasLt k m) => Exists.{0} (LT.lt.{0} Nat Nat.hasLt m n) (fun (hmn : LT.lt.{0} Nat Nat.hasLt m n) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{succ u1} R (fun (z : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Exists.{0} (Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hz : Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) 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(HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) z) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))))))))))))))
 but is expected to have type
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(Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hz : Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) z) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R 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Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R 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Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) z) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))))))))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{1} Nat (fun (n : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{0} (LT.lt.{0} Nat instLTNat m n) (fun (hmn : LT.lt.{0} Nat instLTNat m n) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{succ u1} R (fun (z : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hz : Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) z) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m))) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) z) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) z) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) z) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) z) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))))))))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_three Polynomial.card_support_eq_threeₓ'. -/
 theorem card_support_eq_three :
     f.support.card = 3 ↔

fa256f00

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -472,7 +472,7 @@ theorem card_support_eq {n : ℕ} :
         rw [sum_eq_single, coeff_C_mul, coeff_X_pow_self, mul_one]
         · exact hx i
         · intro j hj hji
-          rw [coeff_C_mul, coeff_X_pow, if_neg (hk.injective.ne hji.symm), mul_zero]
+          rw [coeff_C_mul, coeff_X_pow, if_neg (hk.injective.ne hji.symm), MulZeroClass.mul_zero]
         · exact fun hi => (hi (mem_univ i)).elim
     · intro i
       by_cases hi : ∃ i₀, Fin.castSucc i₀ = i

fa256f00

bump to nightly-2023-03-08-18

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

10f15343

Diff

@@ -102,7 +102,7 @@ theorem eraseLead_add_monomial_natDegree_leadingCoeff (f : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 f)))) f
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 f)))) f
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (Polynomial.eraseLead.{u1} R _inst_1 f) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (Polynomial.leadingCoeff.{u1} R _inst_1 f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (Polynomial.natDegree.{u1} R _inst_1 f)))) f
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_add_C_mul_X_pow Polynomial.eraseLead_add_C_mul_X_powₓ'. -/
 @[simp]
 theorem eraseLead_add_C_mul_X_pow (f : R[X]) :
@@ -126,7 +126,7 @@ theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.ring.{u1} R _inst_2)))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
+  forall {R : Type.{u1}} [_inst_2 : Ring.{u1} R] (f : Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.sub.{u1} R _inst_2)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (Polynomial.mul'.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2))))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (instHPow.{u1, 0} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R _inst_2)))))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R _inst_2)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)))) (Polynomial.eraseLead.{u1} R (Ring.toSemiring.{u1} R _inst_2) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.self_sub_C_mul_X_pow Polynomial.self_sub_C_mul_X_powₓ'. -/
 @[simp]
 theorem self_sub_C_mul_X_pow {R : Type _} [Ring R] (f : R[X]) :
@@ -207,7 +207,7 @@ theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_C Polynomial.eraseLead_Cₓ'. -/
 @[simp]
 theorem eraseLead_C (r : R) : eraseLead (C r) = 0 :=
@@ -232,7 +232,7 @@ theorem eraseLead_X_pow (n : ℕ) : eraseLead (X ^ n : R[X]) = 0 := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))
 Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_C_mul_X_pow Polynomial.eraseLead_C_mul_X_powₓ'. -/
 @[simp]
 theorem eraseLead_C_mul_X_pow (r : R) (n : ℕ) : eraseLead (C r * X ^ n) = 0 := by
@@ -313,7 +313,7 @@ end EraseLead
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (P : (Polynomial.{u1} R _inst_1) -> Prop) (N : Nat), (P (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))) -> (forall (n : Nat) (r : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (LE.le.{0} Nat Nat.hasLe n N) -> (P (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))) -> (forall (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 g)) -> (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 g) N) -> (P f) -> (P g) -> (P (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) f g))) -> (forall (f : Polynomial.{u1} R _inst_1), (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R _inst_1 f) N) -> (P f))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (P : (Polynomial.{u1} R _inst_1) -> Prop) (N : Nat), (P (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (n : Nat) (r : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (LE.le.{0} Nat instLENat n N) -> (P (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))) -> (forall (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 g)) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 g) N) -> (P f) -> (P g) -> (P (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) f g))) -> (forall (f : Polynomial.{u1} R _inst_1), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 f) N) -> (P f))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (P : (Polynomial.{u1} R _inst_1) -> Prop) (N : Nat), (P (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.toOfNat0.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1)))) -> (forall (n : Nat) (r : R), (Ne.{succ u1} R r (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (LE.le.{0} Nat instLENat n N) -> (P (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) r) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))) -> (forall (f : Polynomial.{u1} R _inst_1) (g : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 g)) -> (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 g) N) -> (P f) -> (P g) -> (P (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) f g))) -> (forall (f : Polynomial.{u1} R _inst_1), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R _inst_1 f) N) -> (P f))
 Case conversion may be inaccurate. Consider using '#align polynomial.induction_with_nat_degree_le Polynomial.induction_with_natDegree_leₓ'. -/
 /-- An induction lemma for polynomials. It takes a natural number `N` as a parameter, that is
 required to be at least as big as the `nat_degree` of the polynomial.  This is useful to prove
@@ -415,7 +415,7 @@ open BigOperators
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq' Polynomial.card_support_eq'ₓ'. -/
 theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : Function.Injective k)
     (hx : ∀ i, x i ≠ 0) : (∑ i, C (x i) * X ^ k i).support.card = n :=
@@ -437,7 +437,7 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) n) (Exists.{1} ((Fin n) -> Nat) (fun (k : (Fin n) -> Nat) => Exists.{succ u1} ((Fin n) -> R) (fun (x : (Fin n) -> R) => Exists.{0} (StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.partialOrder n)) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k) (fun (hk : StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.partialOrder n)) (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) k) => Exists.{0} (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) n) (Exists.{1} ((Fin n) -> Nat) (fun (k : (Fin n) -> Nat) => Exists.{succ u1} ((Fin n) -> R) (fun (x : (Fin n) -> R) => Exists.{0} (StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) (fun (hk : StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) => Exists.{0} (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} {n : Nat}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) n) (Exists.{1} ((Fin n) -> Nat) (fun (k : (Fin n) -> Nat) => Exists.{succ u1} ((Fin n) -> R) (fun (x : (Fin n) -> R) => Exists.{0} (StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) (fun (hk : StrictMono.{0, 0} (Fin n) Nat (PartialOrder.toPreorder.{0} (Fin n) (Fin.instPartialOrderFin n)) (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) k) => Exists.{0} (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq Polynomial.card_support_eqₓ'. -/
 theorem card_support_eq {n : ℕ} :
     f.support.card = n ↔
@@ -491,7 +491,7 @@ theorem card_support_eq {n : ℕ} :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (Exists.{1} Nat (fun (k : Nat) => Exists.{succ u1} R (fun (x : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Exists.{1} Nat (fun (k : Nat) => Exists.{succ u1} R (fun (x : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (Exists.{1} Nat (fun (k : Nat) => Exists.{succ u1} R (fun (x : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_one Polynomial.card_support_eq_oneₓ'. -/
 theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x ≠ 0), f = C x * X ^ k :=
   by
@@ -506,7 +506,7 @@ theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (LT.lt.{0} Nat Nat.hasLt k m) (fun (hkm : LT.lt.{0} Nat Nat.hasLt k m) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m)))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m)))))))))))
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) k)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.{u1} R _inst_1) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) y) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) y) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m)))))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_two Polynomial.card_support_eq_twoₓ'. -/
 theorem card_support_eq_two :
     f.support.card = 2 ↔
@@ -525,7 +525,7 @@ theorem card_support_eq_two :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{1} Nat (fun (n : Nat) => Exists.{0} (LT.lt.{0} Nat Nat.hasLt k m) (fun (hkm : LT.lt.{0} Nat Nat.hasLt k m) => Exists.{0} (LT.lt.{0} Nat Nat.hasLt m n) (fun (hmn : LT.lt.{0} Nat Nat.hasLt m n) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{succ u1} R (fun (z : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Exists.{0} (Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) (fun (hz : Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.add'.{u1} R _inst_1)) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) 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(HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) m))) (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) z) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))))))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{1} Nat (fun (n : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{0} (LT.lt.{0} Nat instLTNat m n) (fun (hmn : LT.lt.{0} Nat instLTNat m n) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{succ u1} R (fun (z : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hz : Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) z) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) x) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R 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Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) y) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) z) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R 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+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1}, Iff (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 f)) (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))) (Exists.{1} Nat (fun (k : Nat) => Exists.{1} Nat (fun (m : Nat) => Exists.{1} Nat (fun (n : Nat) => Exists.{0} (LT.lt.{0} Nat instLTNat k m) (fun (hkm : LT.lt.{0} Nat instLTNat k m) => Exists.{0} (LT.lt.{0} Nat instLTNat m n) (fun (hmn : LT.lt.{0} Nat instLTNat m n) => Exists.{succ u1} R (fun (x : R) => Exists.{succ u1} R (fun (y : R) => Exists.{succ u1} R (fun (z : R) => Exists.{0} (Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hx : Ne.{succ u1} R x (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hy : Ne.{succ u1} R y (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Exists.{0} (Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) (fun (hz : Ne.{succ u1} R z (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) => Eq.{succ u1} (Polynomial.{u1} R _inst_1) f (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) z) (Polynomial.{u1} R _inst_1) (instHAdd.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R _inst_1) x) (Polynomial.add'.{u1} R _inst_1)) (HAdd.hAdd.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => Polynomial.{u1} R 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Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) 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_inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n)))))))))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_three Polynomial.card_support_eq_threeₓ'. -/
 theorem card_support_eq_three :
     f.support.card = 3 ↔

fa256f00

bump to nightly-2023-03-08-16

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

593337bd

Diff

@@ -34,98 +34,166 @@ namespace Polynomial
 
 variable {R : Type _} [Semiring R] {f : R[X]}
 
+#print Polynomial.eraseLead /-
 /-- `erase_lead f` for a polynomial `f` is the polynomial obtained by
 subtracting from `f` the leading term of `f`. -/
 def eraseLead (f : R[X]) : R[X] :=
   Polynomial.erase f.natDegree f
 #align polynomial.erase_lead Polynomial.eraseLead
+-/
 
 section EraseLead
 
+/- warning: polynomial.erase_lead_support -> Polynomial.eraseLead_support is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} R _inst_1 (Polynomial.eraseLead.{u1} R _inst_1 f)) (Finset.erase.{0} Nat (fun (a : Nat) (b : Nat) => Nat.decidableEq a b) (Polynomial.support.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 f))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (f : Polynomial.{u1} R _inst_1), Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} R _inst_1 (Polynomial.eraseLead.{u1} R _inst_1 f)) (Finset.erase.{0} Nat (fun (a : Nat) (b : Nat) => instDecidableEqNat a b) (Polynomial.support.{u1} R _inst_1 f) (Polynomial.natDegree.{u1} R _inst_1 f))
+Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_support Polynomial.eraseLead_supportₓ'. -/
 theorem eraseLead_support (f : R[X]) : f.eraseLead.support = f.support.eraseₓ f.natDegree := by
   simp only [erase_lead, support_erase]
 #align polynomial.erase_lead_support Polynomial.eraseLead_support
 
+/- warning: polynomial.erase_lead_coeff -> Polynomial.eraseLead_coeff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (Polynomial.eraseLead.{u1} R _inst_1 f) i) (ite.{succ u1} R (Eq.{1} Nat i (Polynomial.natDegree.{u1} R _inst_1 f)) (Nat.decidableEq i (Polynomial.natDegree.{u1} R _inst_1 f)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))))) (Polynomial.coeff.{u1} R _inst_1 f i))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {f : Polynomial.{u1} R _inst_1} (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R _inst_1 (Polynomial.eraseLead.{u1} R _inst_1 f) i) (ite.{succ u1} R (Eq.{1} Nat i (Polynomial.natDegree.{u1} R _inst_1 f)) (instDecidableEqNat i (Polynomial.natDegree.{u1} R _inst_1 f)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R _inst_1 f i))
+Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_coeff Polynomial.eraseLead_coeffₓ'. -/
 theorem eraseLead_coeff (i : ℕ) : f.eraseLead.coeff i = if i = f.natDegree then 0 else f.coeff i :=
   by simp only [erase_lead, coeff_erase]
 #align polynomial.erase_lead_coeff Polynomial.eraseLead_coeff
 
+/- warning: polynomial.erase_lead_coeff_nat_degree -> Polynomial.eraseLead_coeff_natDegree is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_coeff_nat_degree Polynomial.eraseLead_coeff_natDegreeₓ'. -/
 @[simp]
 theorem eraseLead_coeff_natDegree : f.eraseLead.coeff f.natDegree = 0 := by simp [erase_lead_coeff]
 #align polynomial.erase_lead_coeff_nat_degree Polynomial.eraseLead_coeff_natDegree
 
+#print Polynomial.eraseLead_coeff_of_ne /-
 theorem eraseLead_coeff_of_ne (i : ℕ) (hi : i ≠ f.natDegree) : f.eraseLead.coeff i = f.coeff i := by
   simp [erase_lead_coeff, hi]
 #align polynomial.erase_lead_coeff_of_ne Polynomial.eraseLead_coeff_of_ne
+-/
 
+#print Polynomial.eraseLead_zero /-
 @[simp]
 theorem eraseLead_zero : eraseLead (0 : R[X]) = 0 := by simp only [erase_lead, erase_zero]
 #align polynomial.erase_lead_zero Polynomial.eraseLead_zero
+-/
 
+/- warning: polynomial.erase_lead_add_monomial_nat_degree_leading_coeff -> Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_add_monomial_nat_degree_leading_coeff Polynomial.eraseLead_add_monomial_natDegree_leadingCoeffₓ'. -/
 @[simp]
 theorem eraseLead_add_monomial_natDegree_leadingCoeff (f : R[X]) :
     f.eraseLead + monomial f.natDegree f.leadingCoeff = f :=
   (add_comm _ _).trans (f.monomial_add_erase _)
 #align polynomial.erase_lead_add_monomial_nat_degree_leading_coeff Polynomial.eraseLead_add_monomial_natDegree_leadingCoeff
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_add_C_mul_X_pow Polynomial.eraseLead_add_C_mul_X_powₓ'. -/
 @[simp]
-theorem eraseLead_add_c_mul_x_pow (f : R[X]) :
+theorem eraseLead_add_C_mul_X_pow (f : R[X]) :
     f.eraseLead + C f.leadingCoeff * X ^ f.natDegree = f := by
   rw [C_mul_X_pow_eq_monomial, erase_lead_add_monomial_nat_degree_leading_coeff]
-#align polynomial.erase_lead_add_C_mul_X_pow Polynomial.eraseLead_add_c_mul_x_pow
-
+#align polynomial.erase_lead_add_C_mul_X_pow Polynomial.eraseLead_add_C_mul_X_pow
+
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+Case conversion may be inaccurate. Consider using '#align polynomial.self_sub_monomial_nat_degree_leading_coeff Polynomial.self_sub_monomial_natDegree_leadingCoeffₓ'. -/
 @[simp]
 theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]) :
     f - monomial f.natDegree f.leadingCoeff = f.eraseLead :=
   (eq_sub_iff_add_eq.mpr (eraseLead_add_monomial_natDegree_leadingCoeff f)).symm
 #align polynomial.self_sub_monomial_nat_degree_leading_coeff Polynomial.self_sub_monomial_natDegree_leadingCoeff
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.self_sub_C_mul_X_pow Polynomial.self_sub_C_mul_X_powₓ'. -/
 @[simp]
-theorem self_sub_c_mul_x_pow {R : Type _} [Ring R] (f : R[X]) :
+theorem self_sub_C_mul_X_pow {R : Type _} [Ring R] (f : R[X]) :
     f - C f.leadingCoeff * X ^ f.natDegree = f.eraseLead := by
   rw [C_mul_X_pow_eq_monomial, self_sub_monomial_nat_degree_leading_coeff]
-#align polynomial.self_sub_C_mul_X_pow Polynomial.self_sub_c_mul_x_pow
+#align polynomial.self_sub_C_mul_X_pow Polynomial.self_sub_C_mul_X_pow
 
+#print Polynomial.eraseLead_ne_zero /-
 theorem eraseLead_ne_zero (f0 : 2 ≤ f.support.card) : eraseLead f ≠ 0 :=
   by
   rw [Ne, ← card_support_eq_zero, erase_lead_support]
   exact
     (zero_lt_one.trans_le <| (tsub_le_tsub_right f0 1).trans Finset.pred_card_le_card_erase).Ne.symm
 #align polynomial.erase_lead_ne_zero Polynomial.eraseLead_ne_zero
+-/
 
+#print Polynomial.lt_natDegree_of_mem_eraseLead_support /-
 theorem lt_natDegree_of_mem_eraseLead_support {a : ℕ} (h : a ∈ (eraseLead f).support) :
     a < f.natDegree := by
   rw [erase_lead_support, mem_erase] at h
   exact (le_nat_degree_of_mem_supp a h.2).lt_of_ne h.1
 #align polynomial.lt_nat_degree_of_mem_erase_lead_support Polynomial.lt_natDegree_of_mem_eraseLead_support
+-/
 
+#print Polynomial.ne_natDegree_of_mem_eraseLead_support /-
 theorem ne_natDegree_of_mem_eraseLead_support {a : ℕ} (h : a ∈ (eraseLead f).support) :
     a ≠ f.natDegree :=
   (lt_natDegree_of_mem_eraseLead_support h).Ne
 #align polynomial.ne_nat_degree_of_mem_erase_lead_support Polynomial.ne_natDegree_of_mem_eraseLead_support
+-/
 
+#print Polynomial.natDegree_not_mem_eraseLead_support /-
 theorem natDegree_not_mem_eraseLead_support : f.natDegree ∉ (eraseLead f).support := fun h =>
   ne_natDegree_of_mem_eraseLead_support h rfl
 #align polynomial.nat_degree_not_mem_erase_lead_support Polynomial.natDegree_not_mem_eraseLead_support
+-/
 
+#print Polynomial.eraseLead_support_card_lt /-
 theorem eraseLead_support_card_lt (h : f ≠ 0) : (eraseLead f).support.card < f.support.card :=
   by
   rw [erase_lead_support]
   exact card_lt_card (erase_ssubset <| nat_degree_mem_support_of_nonzero h)
 #align polynomial.erase_lead_support_card_lt Polynomial.eraseLead_support_card_lt
+-/
 
+#print Polynomial.eraseLead_card_support /-
 theorem eraseLead_card_support {c : ℕ} (fc : f.support.card = c) :
     f.eraseLead.support.card = c - 1 := by
   by_cases f0 : f = 0
   · rw [← fc, f0, erase_lead_zero, support_zero, card_empty]
   · rw [erase_lead_support, card_erase_of_mem (nat_degree_mem_support_of_nonzero f0), fc]
 #align polynomial.erase_lead_card_support Polynomial.eraseLead_card_support
+-/
 
+#print Polynomial.eraseLead_card_support' /-
 theorem eraseLead_card_support' {c : ℕ} (fc : f.support.card = c + 1) :
     f.eraseLead.support.card = c :=
   eraseLead_card_support fc
 #align polynomial.erase_lead_card_support' Polynomial.eraseLead_card_support'
+-/
 
+/- warning: polynomial.erase_lead_monomial -> Polynomial.eraseLead_monomial is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (i : Nat) (r : R), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 i) r)) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_monomial Polynomial.eraseLead_monomialₓ'. -/
 @[simp]
 theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
   by
@@ -135,26 +203,43 @@ theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
   · rw [erase_lead, nat_degree_monomial, if_neg hr, erase_monomial]
 #align polynomial.erase_lead_monomial Polynomial.eraseLead_monomial
 
+/- warning: polynomial.erase_lead_C -> Polynomial.eraseLead_C is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_C Polynomial.eraseLead_Cₓ'. -/
 @[simp]
-theorem eraseLead_c (r : R) : eraseLead (C r) = 0 :=
+theorem eraseLead_C (r : R) : eraseLead (C r) = 0 :=
   eraseLead_monomial _ _
-#align polynomial.erase_lead_C Polynomial.eraseLead_c
+#align polynomial.erase_lead_C Polynomial.eraseLead_C
 
+#print Polynomial.eraseLead_X /-
 @[simp]
-theorem eraseLead_x : eraseLead (X : R[X]) = 0 :=
+theorem eraseLead_X : eraseLead (X : R[X]) = 0 :=
   eraseLead_monomial _ _
-#align polynomial.erase_lead_X Polynomial.eraseLead_x
+#align polynomial.erase_lead_X Polynomial.eraseLead_X
+-/
 
+#print Polynomial.eraseLead_X_pow /-
 @[simp]
-theorem eraseLead_x_pow (n : ℕ) : eraseLead (X ^ n : R[X]) = 0 := by
+theorem eraseLead_X_pow (n : ℕ) : eraseLead (X ^ n : R[X]) = 0 := by
   rw [X_pow_eq_monomial, erase_lead_monomial]
-#align polynomial.erase_lead_X_pow Polynomial.eraseLead_x_pow
+#align polynomial.erase_lead_X_pow Polynomial.eraseLead_X_pow
+-/
 
+/- warning: polynomial.erase_lead_C_mul_X_pow -> Polynomial.eraseLead_C_mul_X_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] (r : R) (n : Nat), Eq.{succ u1} (Polynomial.{u1} R _inst_1) (Polynomial.eraseLead.{u1} R _inst_1 (HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) r) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) n))) (OfNat.ofNat.{u1} (Polynomial.{u1} R _inst_1) 0 (OfNat.mk.{u1} (Polynomial.{u1} R _inst_1) 0 (Zero.zero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.zero.{u1} R _inst_1))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.erase_lead_C_mul_X_pow Polynomial.eraseLead_C_mul_X_powₓ'. -/
 @[simp]
-theorem eraseLead_c_mul_x_pow (r : R) (n : ℕ) : eraseLead (C r * X ^ n) = 0 := by
+theorem eraseLead_C_mul_X_pow (r : R) (n : ℕ) : eraseLead (C r * X ^ n) = 0 := by
   rw [C_mul_X_pow_eq_monomial, erase_lead_monomial]
-#align polynomial.erase_lead_C_mul_X_pow Polynomial.eraseLead_c_mul_x_pow
+#align polynomial.erase_lead_C_mul_X_pow Polynomial.eraseLead_C_mul_X_pow
 
+#print Polynomial.eraseLead_add_of_natDegree_lt_left /-
 theorem eraseLead_add_of_natDegree_lt_left {p q : R[X]} (pq : q.natDegree < p.natDegree) :
     (p + q).eraseLead = p.eraseLead + q := by
   ext n
@@ -165,7 +250,9 @@ theorem eraseLead_add_of_natDegree_lt_left {p q : R[X]} (pq : q.natDegree < p.na
     rintro rfl
     exact nd (nat_degree_add_eq_left_of_nat_degree_lt pq)
 #align polynomial.erase_lead_add_of_nat_degree_lt_left Polynomial.eraseLead_add_of_natDegree_lt_left
+-/
 
+#print Polynomial.eraseLead_add_of_natDegree_lt_right /-
 theorem eraseLead_add_of_natDegree_lt_right {p q : R[X]} (pq : p.natDegree < q.natDegree) :
     (p + q).eraseLead = p + q.eraseLead := by
   ext n
@@ -176,21 +263,29 @@ theorem eraseLead_add_of_natDegree_lt_right {p q : R[X]} (pq : p.natDegree < q.n
     rintro rfl
     exact nd (nat_degree_add_eq_right_of_nat_degree_lt pq)
 #align polynomial.erase_lead_add_of_nat_degree_lt_right Polynomial.eraseLead_add_of_natDegree_lt_right
+-/
 
+#print Polynomial.eraseLead_degree_le /-
 theorem eraseLead_degree_le : (eraseLead f).degree ≤ f.degree :=
   f.degree_erase_le _
 #align polynomial.erase_lead_degree_le Polynomial.eraseLead_degree_le
+-/
 
+#print Polynomial.eraseLead_natDegree_le_aux /-
 theorem eraseLead_natDegree_le_aux : (eraseLead f).natDegree ≤ f.natDegree :=
   natDegree_le_natDegree eraseLead_degree_le
 #align polynomial.erase_lead_nat_degree_le_aux Polynomial.eraseLead_natDegree_le_aux
+-/
 
+#print Polynomial.eraseLead_natDegree_lt /-
 theorem eraseLead_natDegree_lt (f0 : 2 ≤ f.support.card) : (eraseLead f).natDegree < f.natDegree :=
   lt_of_le_of_ne eraseLead_natDegree_le_aux <|
     ne_natDegree_of_mem_eraseLead_support <|
       natDegree_mem_support_of_nonzero <| eraseLead_ne_zero f0
 #align polynomial.erase_lead_nat_degree_lt Polynomial.eraseLead_natDegree_lt
+-/
 
+#print Polynomial.eraseLead_natDegree_lt_or_eraseLead_eq_zero /-
 theorem eraseLead_natDegree_lt_or_eraseLead_eq_zero (f : R[X]) :
     (eraseLead f).natDegree < f.natDegree ∨ f.eraseLead = 0 :=
   by
@@ -201,16 +296,25 @@ theorem eraseLead_natDegree_lt_or_eraseLead_eq_zero (f : R[X]) :
   · left
     apply erase_lead_nat_degree_lt (lt_of_not_ge h)
 #align polynomial.erase_lead_nat_degree_lt_or_erase_lead_eq_zero Polynomial.eraseLead_natDegree_lt_or_eraseLead_eq_zero
+-/
 
+#print Polynomial.eraseLead_natDegree_le /-
 theorem eraseLead_natDegree_le (f : R[X]) : (eraseLead f).natDegree ≤ f.natDegree - 1 :=
   by
   rcases f.erase_lead_nat_degree_lt_or_erase_lead_eq_zero with (h | h)
   · exact Nat.le_pred_of_lt h
   · simp only [h, nat_degree_zero, zero_le]
 #align polynomial.erase_lead_nat_degree_le Polynomial.eraseLead_natDegree_le
+-/
 
 end EraseLead
 
+/- warning: polynomial.induction_with_nat_degree_le -> Polynomial.induction_with_natDegree_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.induction_with_nat_degree_le Polynomial.induction_with_natDegree_leₓ'. -/
 /-- An induction lemma for polynomials. It takes a natural number `N` as a parameter, that is
 required to be at least as big as the `nat_degree` of the polynomial.  This is useful to prove
 results where you want to change each term in a polynomial to something else depending on the
@@ -247,6 +351,12 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
       exact Nat.succ_ne_zero _
 #align polynomial.induction_with_nat_degree_le Polynomial.induction_with_natDegree_le
 
+/- warning: polynomial.mono_map_nat_degree_eq -> Polynomial.mono_map_natDegree_eq is a dubious translation:
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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R 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(Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} (k : Nat) (fu : Nat -> Nat), (forall {n : Nat}, (LE.le.{0} Nat instLENat n k) -> (Eq.{1} Nat (fu n) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) -> (forall {n : Nat} {m : Nat}, (LE.le.{0} Nat instLENat k n) -> (LT.lt.{0} Nat instLTNat n m) -> (LT.lt.{0} Nat instLTNat (fu n) (fu m))) -> (forall {f : Polynomial.{u1} R _inst_1}, (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (fu n))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (fu (Polynomial.natDegree.{u1} R _inst_1 p)))
+Case conversion may be inaccurate. Consider using '#align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eqₓ'. -/
 /-- Let `φ : R[x] → S[x]` be an additive map, `k : ℕ` a bound, and `fu : ℕ → ℕ` a
 "sufficiently monotone" map.  Assume also that
 * `φ` maps to `0` all monomials of degree less than `k`,
@@ -272,6 +382,12 @@ theorem mono_map_natDegree_eq {S F : Type _} [Semiring S] [AddMonoidHomClass F R
       · rwa [φ_k (not_le.mp FG), zero_add]
 #align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eq
 
+/- warning: polynomial.map_nat_degree_eq_sub -> Polynomial.map_natDegree_eq_sub is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u2}} {F : Type.{u3}} [_inst_2 : Semiring.{u2} S] [_inst_3 : AddMonoidHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat Nat.hasLt (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u2} (Polynomial.{u2} S _inst_2) (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ f) (OfNat.ofNat.{u2} (Polynomial.{u2} S _inst_2) 0 (OfNat.mk.{u2} (Polynomial.{u2} S _inst_2) 0 (Zero.zero.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.zero.{u2} S _inst_2)))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ (coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n k))) -> (Eq.{1} Nat (Polynomial.natDegree.{u2} S _inst_2 (coeFn.{succ u3, max (succ u1) (succ u2)} F (fun (_x : F) => (Polynomial.{u1} R _inst_1) -> (Polynomial.{u2} S _inst_2)) (FunLike.hasCoeToFun.{succ u3, succ u1, succ u2} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => Polynomial.{u2} S _inst_2) (AddHomClass.toFunLike.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddZeroClass.toHasAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toHasAdd.{u2} (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u3, u1, u2} F (Polynomial.{u1} R _inst_1) (Polynomial.{u2} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u2} (Polynomial.{u2} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u2} (Polynomial.{u2} S _inst_2) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} S _inst_2) (Polynomial.semiring.{u2} S _inst_2)))))) _inst_3))) φ p)) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R _inst_1 p) k))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} {p : Polynomial.{u1} R _inst_1} {k : Nat}, (forall (f : Polynomial.{u1} R _inst_1), (LT.lt.{0} Nat instLTNat (Polynomial.natDegree.{u1} R _inst_1 f) k) -> (Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ f) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) f) (Polynomial.zero.{u3} S _inst_2))))) -> (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => 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(AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R 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+Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_subₓ'. -/
 theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} {k : ℕ} (φ_k : ∀ f : R[X], f.natDegree < k → φ f = 0)
     (φ_mon : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n - k) :
@@ -280,6 +396,12 @@ theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[
     φ_k φ_mon
 #align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_sub
 
+/- warning: polynomial.map_nat_degree_eq_nat_degree -> Polynomial.map_natDegree_eq_natDegree is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {S : Type.{u3}} {F : Type.{u2}} [_inst_2 : Semiring.{u3} S] [_inst_3 : AddMonoidHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))] {φ : F} (p : Polynomial.{u1} R _inst_1), (forall (n : Nat) (c : R), (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : R) => Polynomial.{u1} R _inst_1) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R _inst_1) _inst_1 _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R _inst_1) (Polynomial.module.{u1, u1} R _inst_1 R _inst_1 (Semiring.toModule.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Polynomial.monomial.{u1} R _inst_1 n) c))) n)) -> (Eq.{1} Nat (Polynomial.natDegree.{u3} S _inst_2 (FunLike.coe.{succ u2, succ u1, succ u3} F (Polynomial.{u1} R _inst_1) (fun (_x : Polynomial.{u1} R _inst_1) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Polynomial.{u1} R _inst_1) => Polynomial.{u3} S _inst_2) _x) (AddHomClass.toFunLike.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddZeroClass.toAdd.{u1} (Polynomial.{u1} R _inst_1) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))))) (AddZeroClass.toAdd.{u3} (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2))))))) (AddMonoidHomClass.toAddHomClass.{u2, u1, u3} F (Polynomial.{u1} R _inst_1) (Polynomial.{u3} S _inst_2) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R _inst_1) (AddMonoidWithOne.toAddMonoid.{u1} (Polynomial.{u1} R _inst_1) (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toAddCommMonoidWithOne.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} S _inst_2) (AddMonoidWithOne.toAddMonoid.{u3} (Polynomial.{u3} S _inst_2) (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (NonAssocSemiring.toAddCommMonoidWithOne.{u3} (Polynomial.{u3} S _inst_2) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} S _inst_2) (Polynomial.semiring.{u3} S _inst_2)))))) _inst_3)) φ p)) (Polynomial.natDegree.{u1} R _inst_1 p))
+Case conversion may be inaccurate. Consider using '#align polynomial.map_nat_degree_eq_nat_degree Polynomial.map_natDegree_eq_natDegreeₓ'. -/
 theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]]
     {φ : F} (p) (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n) :
     (φ p).natDegree = p.natDegree :=
@@ -289,6 +411,12 @@ theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClas
 
 open BigOperators
 
+/- warning: polynomial.card_support_eq' -> Polynomial.card_support_eq' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.mul'.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) => R -> (Polynomial.{u1} R _inst_1)) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : Semiring.{u1} R] {n : Nat} (k : (Fin n) -> Nat) (x : (Fin n) -> R), (Function.Injective.{1, 1} (Fin n) Nat k) -> (forall (i : Fin n), Ne.{succ u1} R (x i) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))))) -> (Eq.{1} Nat (Finset.card.{0} Nat (Polynomial.support.{u1} R _inst_1 (Finset.sum.{u1, 0} (Polynomial.{u1} R _inst_1) (Fin n) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (Finset.univ.{0} (Fin n) (Fin.fintype n)) (fun (i : Fin n) => HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.{u1} R _inst_1) (Polynomial.{u1} R _inst_1) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) (x i)) (Polynomial.mul'.{u1} R _inst_1)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => Polynomial.{u1} R _inst_1) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toMul.{u1} (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))) R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)) (RingHom.instRingHomClassRingHom.{u1, u1} R (Polynomial.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} R _inst_1) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1)))))) (Polynomial.C.{u1} R _inst_1) (x i)) (HPow.hPow.{u1, 0, u1} (Polynomial.{u1} R _inst_1) Nat (Polynomial.{u1} R _inst_1) (instHPow.{u1, 0} (Polynomial.{u1} R _inst_1) Nat (Monoid.Pow.{u1} (Polynomial.{u1} R _inst_1) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R _inst_1) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R _inst_1) (Polynomial.semiring.{u1} R _inst_1))))) (Polynomial.X.{u1} R _inst_1) (k i)))))) n)
+Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq' Polynomial.card_support_eq'ₓ'. -/
 theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : Function.Injective k)
     (hx : ∀ i, x i ≠ 0) : (∑ i, C (x i) * X ^ k i).support.card = n :=
   by
@@ -305,6 +433,12 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
     · exact fun m hm hmj => if_neg fun h => hmj.symm (hk h)
 #align polynomial.card_support_eq' Polynomial.card_support_eq'
 
+/- warning: polynomial.card_support_eq -> Polynomial.card_support_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq Polynomial.card_support_eqₓ'. -/
 theorem card_support_eq {n : ℕ} :
     f.support.card = n ↔
       ∃ (k : Fin n → ℕ)(x : Fin n → R)(hk : StrictMono k)(hx : ∀ i, x i ≠ 0),
@@ -353,6 +487,12 @@ theorem card_support_eq {n : ℕ} :
       all_goals exact H
 #align polynomial.card_support_eq Polynomial.card_support_eq
 
+/- warning: polynomial.card_support_eq_one -> Polynomial.card_support_eq_one is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_one Polynomial.card_support_eq_oneₓ'. -/
 theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x ≠ 0), f = C x * X ^ k :=
   by
   refine' ⟨fun h => _, _⟩
@@ -362,6 +502,12 @@ theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x
     rw [support_C_mul_X_pow k hx, card_singleton]
 #align polynomial.card_support_eq_one Polynomial.card_support_eq_one
 
+/- warning: polynomial.card_support_eq_two -> Polynomial.card_support_eq_two is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_two Polynomial.card_support_eq_twoₓ'. -/
 theorem card_support_eq_two :
     f.support.card = 2 ↔
       ∃ (k m : ℕ)(hkm : k < m)(x y : R)(hx : x ≠ 0)(hy : y ≠ 0), f = C x * X ^ k + C y * X ^ m :=
@@ -375,6 +521,12 @@ theorem card_support_eq_two :
     exact card_support_binomial hkm.ne hx hy
 #align polynomial.card_support_eq_two Polynomial.card_support_eq_two
 
+/- warning: polynomial.card_support_eq_three -> Polynomial.card_support_eq_three is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.card_support_eq_three Polynomial.card_support_eq_threeₓ'. -/
 theorem card_support_eq_three :
     f.support.card = 3 ↔
       ∃ (k m n : ℕ)(hkm : k < m)(hmn : m < n)(x y z : R)(hx : x ≠ 0)(hy : y ≠ 0)(hz : z ≠ 0),

fa256f00

bump to nightly-2023-03-08-10

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

422cc012

Diff

@@ -70,7 +70,7 @@ theorem eraseLead_add_monomial_natDegree_leadingCoeff (f : R[X]) :
 
 @[simp]
 theorem eraseLead_add_c_mul_x_pow (f : R[X]) :
-    f.eraseLead + c f.leadingCoeff * x ^ f.natDegree = f := by
+    f.eraseLead + C f.leadingCoeff * X ^ f.natDegree = f := by
   rw [C_mul_X_pow_eq_monomial, erase_lead_add_monomial_nat_degree_leading_coeff]
 #align polynomial.erase_lead_add_C_mul_X_pow Polynomial.eraseLead_add_c_mul_x_pow
 
@@ -82,7 +82,7 @@ theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]
 
 @[simp]
 theorem self_sub_c_mul_x_pow {R : Type _} [Ring R] (f : R[X]) :
-    f - c f.leadingCoeff * x ^ f.natDegree = f.eraseLead := by
+    f - C f.leadingCoeff * X ^ f.natDegree = f.eraseLead := by
   rw [C_mul_X_pow_eq_monomial, self_sub_monomial_nat_degree_leading_coeff]
 #align polynomial.self_sub_C_mul_X_pow Polynomial.self_sub_c_mul_x_pow
 
@@ -136,22 +136,22 @@ theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 :=
 #align polynomial.erase_lead_monomial Polynomial.eraseLead_monomial
 
 @[simp]
-theorem eraseLead_c (r : R) : eraseLead (c r) = 0 :=
+theorem eraseLead_c (r : R) : eraseLead (C r) = 0 :=
   eraseLead_monomial _ _
 #align polynomial.erase_lead_C Polynomial.eraseLead_c
 
 @[simp]
-theorem eraseLead_x : eraseLead (x : R[X]) = 0 :=
+theorem eraseLead_x : eraseLead (X : R[X]) = 0 :=
   eraseLead_monomial _ _
 #align polynomial.erase_lead_X Polynomial.eraseLead_x
 
 @[simp]
-theorem eraseLead_x_pow (n : ℕ) : eraseLead (x ^ n : R[X]) = 0 := by
+theorem eraseLead_x_pow (n : ℕ) : eraseLead (X ^ n : R[X]) = 0 := by
   rw [X_pow_eq_monomial, erase_lead_monomial]
 #align polynomial.erase_lead_X_pow Polynomial.eraseLead_x_pow
 
 @[simp]
-theorem eraseLead_c_mul_x_pow (r : R) (n : ℕ) : eraseLead (c r * x ^ n) = 0 := by
+theorem eraseLead_c_mul_x_pow (r : R) (n : ℕ) : eraseLead (C r * X ^ n) = 0 := by
   rw [C_mul_X_pow_eq_monomial, erase_lead_monomial]
 #align polynomial.erase_lead_C_mul_X_pow Polynomial.eraseLead_c_mul_x_pow
 
@@ -216,7 +216,7 @@ required to be at least as big as the `nat_degree` of the polynomial.  This is u
 results where you want to change each term in a polynomial to something else depending on the
 `nat_degree` of the polynomial itself and not on the specific `nat_degree` of each term. -/
 theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
-    (P_C_mul_pow : ∀ n : ℕ, ∀ r : R, r ≠ 0 → n ≤ N → P (c r * x ^ n))
+    (P_C_mul_pow : ∀ n : ℕ, ∀ r : R, r ≠ 0 → n ≤ N → P (C r * X ^ n))
     (P_C_add : ∀ f g : R[X], f.natDegree < g.natDegree → g.natDegree ≤ N → P f → P g → P (f + g)) :
     ∀ f : R[X], f.natDegree ≤ N → P f := by
   intro f df
@@ -290,7 +290,7 @@ theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClas
 open BigOperators
 
 theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : Function.Injective k)
-    (hx : ∀ i, x i ≠ 0) : (∑ i, c (x i) * x ^ k i).support.card = n :=
+    (hx : ∀ i, x i ≠ 0) : (∑ i, C (x i) * X ^ k i).support.card = n :=
   by
   suffices (∑ i, C (x i) * X ^ k i).support = image k univ by
     rw [this, univ.card_image_of_injective hk, card_fin]
@@ -308,7 +308,7 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
 theorem card_support_eq {n : ℕ} :
     f.support.card = n ↔
       ∃ (k : Fin n → ℕ)(x : Fin n → R)(hk : StrictMono k)(hx : ∀ i, x i ≠ 0),
-        f = ∑ i, c (x i) * x ^ k i :=
+        f = ∑ i, C (x i) * X ^ k i :=
   by
   refine' ⟨_, fun ⟨k, x, hk, hx, hf⟩ => hf.symm ▸ card_support_eq' k x hk.Injective hx⟩
   induction' n with n hn generalizing f
@@ -353,7 +353,7 @@ theorem card_support_eq {n : ℕ} :
       all_goals exact H
 #align polynomial.card_support_eq Polynomial.card_support_eq
 
-theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x ≠ 0), f = c x * x ^ k :=
+theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x ≠ 0), f = C x * X ^ k :=
   by
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h
@@ -364,7 +364,7 @@ theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x
 
 theorem card_support_eq_two :
     f.support.card = 2 ↔
-      ∃ (k m : ℕ)(hkm : k < m)(x y : R)(hx : x ≠ 0)(hy : y ≠ 0), f = c x * x ^ k + c y * x ^ m :=
+      ∃ (k m : ℕ)(hkm : k < m)(x y : R)(hx : x ≠ 0)(hy : y ≠ 0), f = C x * X ^ k + C y * X ^ m :=
   by
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h
@@ -378,7 +378,7 @@ theorem card_support_eq_two :
 theorem card_support_eq_three :
     f.support.card = 3 ↔
       ∃ (k m n : ℕ)(hkm : k < m)(hmn : m < n)(x y z : R)(hx : x ≠ 0)(hy : y ≠ 0)(hz : z ≠ 0),
-        f = c x * x ^ k + c y * x ^ m + c z * x ^ n :=
+        f = C x * X ^ k + C y * X ^ m + C z * X ^ n :=
   by
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h

fa256f00

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

fa256f00

move(Polynomial): Move out of Data (#11751)

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

56e439ec

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa, Alex Meiburg
 -/
 import Mathlib.Algebra.BigOperators.Fin
-import Mathlib.Data.Polynomial.Degree.Lemmas
+import Mathlib.Algebra.Polynomial.Degree.Lemmas
 
 #align_import data.polynomial.erase_lead from "leanprover-community/mathlib"@"fa256f00ce018e7b40e1dc756e403c86680bf448"

fa256f00

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -300,7 +300,7 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
     · convert P_C_mul_pow f.natDegree f.leadingCoeff ?_ df using 1
       · convert zero_add (C (leadingCoeff f) * X ^ f.natDegree)
         rw [← card_support_eq_zero, card_support_eraseLead' f0]
-      · rw [leadingCoeff_ne_zero, Ne.def, ← card_support_eq_zero, f0]
+      · rw [leadingCoeff_ne_zero, Ne, ← card_support_eq_zero, f0]
         exact zero_ne_one.symm
     refine' P_C_add f.eraseLead _ _ _ _ _
     · refine' (eraseLead_natDegree_lt _).trans_le (le_of_eq _)
@@ -311,7 +311,7 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
     · exact (natDegree_C_mul_X_pow_le f.leadingCoeff f.natDegree).trans df
     · exact hc _ (eraseLead_natDegree_le_aux.trans df) (card_support_eraseLead' f0)
     · refine' P_C_mul_pow _ _ _ df
-      rw [Ne.def, leadingCoeff_eq_zero, ← card_support_eq_zero, f0]
+      rw [Ne, leadingCoeff_eq_zero, ← card_support_eq_zero, f0]
       exact Nat.succ_ne_zero _
 #align polynomial.induction_with_nat_degree_le Polynomial.induction_with_natDegree_le

fa256f00

chore: remove @[simp] from tsub_eq_zero_iff_le (#10474)

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

7fa9bfd0

Diff

@@ -346,7 +346,7 @@ theorem map_natDegree_eq_sub {S F : Type*} [Semiring S]
     {p : R[X]} {k : ℕ} (φ_k : ∀ f : R[X], f.natDegree < k → φ f = 0)
     (φ_mon : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n - k) :
     (φ p).natDegree = p.natDegree - k :=
-  mono_map_natDegree_eq k (fun j => j - k) (by simp)
+  mono_map_natDegree_eq k (fun j => j - k) (by simp_all)
     (@fun m n h => (tsub_lt_tsub_iff_right h).mpr)
     (φ_k _) φ_mon
 #align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_sub

fa256f00

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

`simp` not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

c6a73d4f

Diff

@@ -320,7 +320,8 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
 * `φ` maps to `0` all monomials of degree less than `k`,
 * `φ` maps each monomial `m` in `R[x]` to a polynomial `φ m` of degree `fu (deg m)`.
 Then, `φ` maps each polynomial `p` in `R[x]` to a polynomial of degree `fu (deg p)`. -/
-theorem mono_map_natDegree_eq {S F : Type*} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
+theorem mono_map_natDegree_eq {S F : Type*} [Semiring S]
+    [FunLike F R[X] S[X]] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} (k : ℕ) (fu : ℕ → ℕ) (fu0 : ∀ {n}, n ≤ k → fu n = 0)
     (fc : ∀ {n m}, k ≤ n → n < m → fu n < fu m) (φ_k : ∀ {f : R[X]}, f.natDegree < k → φ f = 0)
     (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = fu n) :
@@ -340,7 +341,8 @@ theorem mono_map_natDegree_eq {S F : Type*} [Semiring S] [AddMonoidHomClass F R[
       · rwa [φ_k (not_le.mp FG), zero_add]
 #align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eq
 
-theorem map_natDegree_eq_sub {S F : Type*} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
+theorem map_natDegree_eq_sub {S F : Type*} [Semiring S]
+    [FunLike F R[X] S[X]] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} {k : ℕ} (φ_k : ∀ f : R[X], f.natDegree < k → φ f = 0)
     (φ_mon : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n - k) :
     (φ p).natDegree = p.natDegree - k :=
@@ -349,7 +351,8 @@ theorem map_natDegree_eq_sub {S F : Type*} [Semiring S] [AddMonoidHomClass F R[X
     (φ_k _) φ_mon
 #align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_sub
 
-theorem map_natDegree_eq_natDegree {S F : Type*} [Semiring S] [AddMonoidHomClass F R[X] S[X]]
+theorem map_natDegree_eq_natDegree {S F : Type*} [Semiring S]
+    [FunLike F R[X] S[X]] [AddMonoidHomClass F R[X] S[X]]
     {φ : F} (p) (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n) :
     (φ p).natDegree = p.natDegree :=
   (map_natDegree_eq_sub (fun f h => (Nat.not_lt_zero _ h).elim) (by simpa)).trans

fa256f00

feat: Lemmas relating Polynomial.eraseLead and nextCoeff. (#9083)

Some little theorems relating eraseLead and nextCoeff to each other. Also includes monomial_sub and card_support_mul which could be of independent interest.

Co-authored-by: Alex Meiburg <timeroot.alex@gmail.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

716dfd4a

Diff

@@ -1,10 +1,10 @@
 /-
 Copyright (c) 2020 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Damiano Testa
+Authors: Damiano Testa, Alex Meiburg
 -/
 import Mathlib.Algebra.BigOperators.Fin
-import Mathlib.Data.Polynomial.Degree.Definitions
+import Mathlib.Data.Polynomial.Degree.Lemmas
 
 #align_import data.polynomial.erase_lead from "leanprover-community/mathlib"@"fa256f00ce018e7b40e1dc756e403c86680bf448"
 
@@ -111,17 +111,36 @@ theorem eraseLead_support_card_lt (h : f ≠ 0) : (eraseLead f).support.card < f
   exact card_lt_card (erase_ssubset <| natDegree_mem_support_of_nonzero h)
 #align polynomial.erase_lead_support_card_lt Polynomial.eraseLead_support_card_lt
 
-theorem eraseLead_card_support {c : ℕ} (fc : f.support.card = c) :
-    f.eraseLead.support.card = c - 1 := by
-  by_cases f0 : f = 0
-  · rw [← fc, f0, eraseLead_zero, support_zero, card_empty]
-  · rw [eraseLead_support, card_erase_of_mem (natDegree_mem_support_of_nonzero f0), fc]
-#align polynomial.erase_lead_card_support Polynomial.eraseLead_card_support
+theorem card_support_eraseLead_add_one (h : f ≠ 0) :
+    f.eraseLead.support.card + 1 = f.support.card := by
+  set c := f.support.card with hc
+  cases h₁ : c
+  case zero =>
+    by_contra
+    exact h (card_support_eq_zero.mp h₁)
+  case succ =>
+    rw [eraseLead_support, card_erase_of_mem (natDegree_mem_support_of_nonzero h), ← hc, h₁]
+    rfl
+
+@[simp]
+theorem card_support_eraseLead : f.eraseLead.support.card = f.support.card - 1 := by
+  by_cases hf : f = 0
+  · rw [hf, eraseLead_zero, support_zero, card_empty]
+  · rw [← card_support_eraseLead_add_one hf, add_tsub_cancel_right]
 
-theorem eraseLead_card_support' {c : ℕ} (fc : f.support.card = c + 1) :
-    f.eraseLead.support.card = c :=
-  eraseLead_card_support fc
-#align polynomial.erase_lead_card_support' Polynomial.eraseLead_card_support'
+theorem card_support_eraseLead' {c : ℕ} (fc : f.support.card = c + 1) :
+    f.eraseLead.support.card = c := by
+  rw [card_support_eraseLead, fc, add_tsub_cancel_right]
+#align polynomial.erase_lead_card_support' Polynomial.card_support_eraseLead'
+
+theorem card_support_eq_one_of_eraseLead_eq_zero (h₀ : f ≠ 0) (h₁ : f.eraseLead = 0) :
+    f.support.card = 1 :=
+  (card_support_eq_zero.mpr h₁ ▸ card_support_eraseLead_add_one h₀).symm
+
+theorem card_support_le_one_of_eraseLead_eq_zero (h : f.eraseLead = 0) : f.support.card ≤ 1 := by
+  by_cases hpz : f = 0
+  case pos => simp [hpz]
+  case neg => exact le_of_eq (card_support_eq_one_of_eraseLead_eq_zero hpz h)
 
 @[simp]
 theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 := by
@@ -156,6 +175,9 @@ theorem eraseLead_C_mul_X_pow (r : R) (n : ℕ) : eraseLead (C r * X ^ n) = 0 :=
 set_option linter.uppercaseLean3 false in
 #align polynomial.erase_lead_C_mul_X_pow Polynomial.eraseLead_C_mul_X_pow
 
+@[simp] lemma eraseLead_C_mul_X (r : R) : eraseLead (C r * X) = 0 := by
+  simpa using eraseLead_C_mul_X_pow _ 1
+
 theorem eraseLead_add_of_natDegree_lt_left {p q : R[X]} (pq : q.natDegree < p.natDegree) :
     (p + q).eraseLead = p.eraseLead + q := by
   ext n
@@ -192,6 +214,11 @@ theorem eraseLead_natDegree_lt (f0 : 2 ≤ f.support.card) : (eraseLead f).natDe
       natDegree_mem_support_of_nonzero <| eraseLead_ne_zero f0
 #align polynomial.erase_lead_nat_degree_lt Polynomial.eraseLead_natDegree_lt
 
+theorem natDegree_pos_of_eraseLead_ne_zero (h : f.eraseLead ≠ 0) : 0 < f.natDegree := by
+  by_contra h₂
+  rw [eq_C_of_natDegree_eq_zero (Nat.eq_zero_of_not_pos h₂)] at h
+  simp at h
+
 theorem eraseLead_natDegree_lt_or_eraseLead_eq_zero (f : R[X]) :
     (eraseLead f).natDegree < f.natDegree ∨ f.eraseLead = 0 := by
   by_cases h : f.support.card ≤ 1
@@ -208,6 +235,48 @@ theorem eraseLead_natDegree_le (f : R[X]) : (eraseLead f).natDegree ≤ f.natDeg
   · simp only [h, natDegree_zero, zero_le]
 #align polynomial.erase_lead_nat_degree_le Polynomial.eraseLead_natDegree_le
 
+lemma natDegree_eraseLead (h : f.nextCoeff ≠ 0) : f.eraseLead.natDegree = f.natDegree - 1 := by
+  have := natDegree_pos_of_nextCoeff_ne_zero h
+  refine f.eraseLead_natDegree_le.antisymm $ le_natDegree_of_ne_zero ?_
+  rwa [eraseLead_coeff_of_ne _ (tsub_lt_self _ _).ne, ← nextCoeff_of_natDegree_pos]
+  all_goals positivity
+
+lemma natDegree_eraseLead_add_one (h : f.nextCoeff ≠ 0) :
+    f.eraseLead.natDegree + 1 = f.natDegree := by
+  rw [natDegree_eraseLead h, tsub_add_cancel_of_le]
+  exact natDegree_pos_of_nextCoeff_ne_zero h
+
+theorem natDegree_eraseLead_le_of_nextCoeff_eq_zero (h : f.nextCoeff = 0) :
+    f.eraseLead.natDegree ≤ f.natDegree - 2 := by
+  refine natDegree_le_pred (n := f.natDegree - 1) (eraseLead_natDegree_le f) ?_
+  rw [nextCoeff_eq_zero, natDegree_eq_zero] at h
+  obtain ⟨a, rfl⟩ | ⟨hf, h⟩ := h
+  · simp
+  rw [eraseLead_coeff_of_ne _ (tsub_lt_self hf zero_lt_one).ne, ← nextCoeff_of_natDegree_pos hf]
+  simp [nextCoeff_eq_zero, h, eq_zero_or_pos]
+
+lemma two_le_natDegree_of_nextCoeff_eraseLead (hlead : f.eraseLead ≠ 0) (hnext : f.nextCoeff = 0) :
+    2 ≤ f.natDegree := by
+  contrapose! hlead
+  rw [Nat.lt_succ_iff, Nat.le_one_iff_eq_zero_or_eq_one, natDegree_eq_zero, natDegree_eq_one]
+    at hlead
+  obtain ⟨a, rfl⟩ | ⟨a, ha, b, rfl⟩ := hlead
+  · simp
+  · rw [nextCoeff_C_mul_X_add_C ha] at hnext
+    subst b
+    simp
+
+theorem leadingCoeff_eraseLead_eq_nextCoeff (h : f.nextCoeff ≠ 0) :
+    f.eraseLead.leadingCoeff = f.nextCoeff := by
+  have := natDegree_pos_of_nextCoeff_ne_zero h
+  rw [leadingCoeff, nextCoeff, natDegree_eraseLead h, if_neg,
+    eraseLead_coeff_of_ne _ (tsub_lt_self _ _).ne]
+  all_goals positivity
+
+theorem nextCoeff_eq_zero_of_eraseLead_eq_zero (h : f.eraseLead = 0) : f.nextCoeff = 0 := by
+  by_contra h₂
+  exact leadingCoeff_ne_zero.mp (leadingCoeff_eraseLead_eq_nextCoeff h₂ ▸ h₂) h
+
 end EraseLead
 
 /-- An induction lemma for polynomials. It takes a natural number `N` as a parameter, that is
@@ -230,7 +299,7 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
     cases c
     · convert P_C_mul_pow f.natDegree f.leadingCoeff ?_ df using 1
       · convert zero_add (C (leadingCoeff f) * X ^ f.natDegree)
-        rw [← card_support_eq_zero, eraseLead_card_support f0]
+        rw [← card_support_eq_zero, card_support_eraseLead' f0]
       · rw [leadingCoeff_ne_zero, Ne.def, ← card_support_eq_zero, f0]
         exact zero_ne_one.symm
     refine' P_C_add f.eraseLead _ _ _ _ _
@@ -240,7 +309,7 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
         rintro rfl
         simp at f0
     · exact (natDegree_C_mul_X_pow_le f.leadingCoeff f.natDegree).trans df
-    · exact hc _ (eraseLead_natDegree_le_aux.trans df) (eraseLead_card_support f0)
+    · exact hc _ (eraseLead_natDegree_le_aux.trans df) (card_support_eraseLead' f0)
     · refine' P_C_mul_pow _ _ _ df
       rw [Ne.def, leadingCoeff_eq_zero, ← card_support_eq_zero, f0]
       exact Nat.succ_ne_zero _
@@ -312,7 +381,7 @@ theorem card_support_eq {n : ℕ} :
   induction' n with n hn generalizing f
   · exact fun hf => ⟨0, 0, fun x => x.elim0, fun x => x.elim0, card_support_eq_zero.mp hf⟩
   · intro h
-    obtain ⟨k, x, hk, hx, hf⟩ := hn (eraseLead_card_support' h)
+    obtain ⟨k, x, hk, hx, hf⟩ := hn (card_support_eraseLead' h)
     have H : ¬∃ k : Fin n, Fin.castSucc k = Fin.last n := by
       rintro ⟨i, hi⟩
       exact i.castSucc_lt_last.ne hi

fa256f00

fix: patch for std4#195 (more succ/pred lemmas for Nat) (#6203)

cdcad962

Diff

@@ -204,7 +204,7 @@ theorem eraseLead_natDegree_lt_or_eraseLead_eq_zero (f : R[X]) :
 
 theorem eraseLead_natDegree_le (f : R[X]) : (eraseLead f).natDegree ≤ f.natDegree - 1 := by
   rcases f.eraseLead_natDegree_lt_or_eraseLead_eq_zero with (h | h)
-  · exact Nat.le_pred_of_lt h
+  · exact Nat.le_sub_one_of_lt h
   · simp only [h, natDegree_zero, zero_le]
 #align polynomial.erase_lead_nat_degree_le Polynomial.eraseLead_natDegree_le

fa256f00

refactor(Data/Polynomial): remove open Classical (#7706)

This doesn't change any polynomial operations, but:

Makes some Decidable values computable (otherwise, they're pointless!)
Add a few missing arguments to lemmas here and there to make them more general

This is exhaustive, within the directories it touches.

Once again, the use of letI := Classical.decEq R instead of classical here is because of the weird style of proofs in these files, where if is preferred to by_cases.

4a7ff0e3

Diff

@@ -23,7 +23,7 @@ and thus works for polynomials over semirings as well as rings.
 
 noncomputable section
 
-open Classical Polynomial
+open Polynomial
 
 open Polynomial Finset
 
@@ -125,6 +125,7 @@ theorem eraseLead_card_support' {c : ℕ} (fc : f.support.card = c + 1) :
 
 @[simp]
 theorem eraseLead_monomial (i : ℕ) (r : R) : eraseLead (monomial i r) = 0 := by
+  classical
   by_cases hr : r = 0
   · subst r
     simp only [monomial_zero_right, eraseLead_zero]

fa256f00

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -29,7 +29,7 @@ open Polynomial Finset
 
 namespace Polynomial
 
-variable {R : Type _} [Semiring R] {f : R[X]}
+variable {R : Type*} [Semiring R] {f : R[X]}
 
 /-- `eraseLead f` for a polynomial `f` is the polynomial obtained by
 subtracting from `f` the leading term of `f`. -/
@@ -73,13 +73,13 @@ set_option linter.uppercaseLean3 false in
 #align polynomial.erase_lead_add_C_mul_X_pow Polynomial.eraseLead_add_C_mul_X_pow
 
 @[simp]
-theorem self_sub_monomial_natDegree_leadingCoeff {R : Type _} [Ring R] (f : R[X]) :
+theorem self_sub_monomial_natDegree_leadingCoeff {R : Type*} [Ring R] (f : R[X]) :
     f - monomial f.natDegree f.leadingCoeff = f.eraseLead :=
   (eq_sub_iff_add_eq.mpr (eraseLead_add_monomial_natDegree_leadingCoeff f)).symm
 #align polynomial.self_sub_monomial_nat_degree_leading_coeff Polynomial.self_sub_monomial_natDegree_leadingCoeff
 
 @[simp]
-theorem self_sub_C_mul_X_pow {R : Type _} [Ring R] (f : R[X]) :
+theorem self_sub_C_mul_X_pow {R : Type*} [Ring R] (f : R[X]) :
     f - C f.leadingCoeff * X ^ f.natDegree = f.eraseLead := by
   rw [C_mul_X_pow_eq_monomial, self_sub_monomial_natDegree_leadingCoeff]
 set_option linter.uppercaseLean3 false in
@@ -250,7 +250,7 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
 * `φ` maps to `0` all monomials of degree less than `k`,
 * `φ` maps each monomial `m` in `R[x]` to a polynomial `φ m` of degree `fu (deg m)`.
 Then, `φ` maps each polynomial `p` in `R[x]` to a polynomial of degree `fu (deg p)`. -/
-theorem mono_map_natDegree_eq {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
+theorem mono_map_natDegree_eq {S F : Type*} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} (k : ℕ) (fu : ℕ → ℕ) (fu0 : ∀ {n}, n ≤ k → fu n = 0)
     (fc : ∀ {n m}, k ≤ n → n < m → fu n < fu m) (φ_k : ∀ {f : R[X]}, f.natDegree < k → φ f = 0)
     (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = fu n) :
@@ -270,7 +270,7 @@ theorem mono_map_natDegree_eq {S F : Type _} [Semiring S] [AddMonoidHomClass F R
       · rwa [φ_k (not_le.mp FG), zero_add]
 #align polynomial.mono_map_nat_degree_eq Polynomial.mono_map_natDegree_eq
 
-theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
+theorem map_natDegree_eq_sub {S F : Type*} [Semiring S] [AddMonoidHomClass F R[X] S[X]] {φ : F}
     {p : R[X]} {k : ℕ} (φ_k : ∀ f : R[X], f.natDegree < k → φ f = 0)
     (φ_mon : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n - k) :
     (φ p).natDegree = p.natDegree - k :=
@@ -279,7 +279,7 @@ theorem map_natDegree_eq_sub {S F : Type _} [Semiring S] [AddMonoidHomClass F R[
     (φ_k _) φ_mon
 #align polynomial.map_nat_degree_eq_sub Polynomial.map_natDegree_eq_sub
 
-theorem map_natDegree_eq_natDegree {S F : Type _} [Semiring S] [AddMonoidHomClass F R[X] S[X]]
+theorem map_natDegree_eq_natDegree {S F : Type*} [Semiring S] [AddMonoidHomClass F R[X] S[X]]
     {φ : F} (p) (φ_mon_nat : ∀ n c, c ≠ 0 → (φ (monomial n c)).natDegree = n) :
     (φ p).natDegree = p.natDegree :=
   (map_natDegree_eq_sub (fun f h => (Nat.not_lt_zero _ h).elim) (by simpa)).trans

fa256f00

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Damiano Testa. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Damiano Testa
-
-! This file was ported from Lean 3 source module data.polynomial.erase_lead
-! leanprover-community/mathlib commit fa256f00ce018e7b40e1dc756e403c86680bf448
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.BigOperators.Fin
 import Mathlib.Data.Polynomial.Degree.Definitions
 
+#align_import data.polynomial.erase_lead from "leanprover-community/mathlib"@"fa256f00ce018e7b40e1dc756e403c86680bf448"
+
 /-!
 # Erase the leading term of a univariate polynomial

fa256f00

chore: bump to nightly-2023-07-01 (#5409)

depends on: https://github.com/leanprover/std4/pull/163
depends on: #5584
depends on: #5715
depends on: #5729
depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

906f7221

Diff

@@ -315,22 +315,22 @@ theorem card_support_eq {n : ℕ} :
   · exact fun hf => ⟨0, 0, fun x => x.elim0, fun x => x.elim0, card_support_eq_zero.mp hf⟩
   · intro h
     obtain ⟨k, x, hk, hx, hf⟩ := hn (eraseLead_card_support' h)
-    have H : ¬∃ k : Fin n, Fin.castSuccEmb k = Fin.last n := by
+    have H : ¬∃ k : Fin n, Fin.castSucc k = Fin.last n := by
       rintro ⟨i, hi⟩
-      exact i.castSuccEmb_lt_last.ne hi
+      exact i.castSucc_lt_last.ne hi
     refine'
-      ⟨Function.extend Fin.castSuccEmb k fun _ => f.natDegree,
-        Function.extend Fin.castSuccEmb x fun _ => f.leadingCoeff, _, _, _⟩
+      ⟨Function.extend Fin.castSucc k fun _ => f.natDegree,
+        Function.extend Fin.castSucc x fun _ => f.leadingCoeff, _, _, _⟩
     · intro i j hij
-      have hi : i ∈ Set.range (Fin.castSuccEmb : Fin n ↪o Fin (n + 1)) := by
-        rw [Fin.range_castSuccEmb, Set.mem_def]
+      have hi : i ∈ Set.range (Fin.castSucc : Fin n → Fin (n + 1)) := by
+        rw [Fin.range_castSucc, Set.mem_def]
         exact lt_of_lt_of_le hij (Nat.lt_succ_iff.mp j.2)
       obtain ⟨i, rfl⟩ := hi
-      rw [Fin.castSuccEmb.injective.extend_apply]
-      by_cases hj : ∃ j₀, Fin.castSuccEmb j₀ = j
+      rw [Fin.strictMono_castSucc.injective.extend_apply]
+      by_cases hj : ∃ j₀, Fin.castSucc j₀ = j
       · obtain ⟨j, rfl⟩ := hj
-        rwa [Fin.castSuccEmb.injective.extend_apply, hk.lt_iff_lt,
-          ← Fin.castSuccEmb_lt_castSuccEmb_iff]
+        rwa [Fin.strictMono_castSucc.injective.extend_apply, hk.lt_iff_lt,
+          ← Fin.castSucc_lt_castSucc_iff]
       · rw [Function.extend_apply' _ _ _ hj]
         apply lt_natDegree_of_mem_eraseLead_support
         rw [mem_support_iff, hf, finset_sum_coeff]
@@ -340,14 +340,14 @@ theorem card_support_eq {n : ℕ} :
           rw [coeff_C_mul, coeff_X_pow, if_neg (hk.injective.ne hji.symm), mul_zero]
         · exact fun hi => (hi (mem_univ i)).elim
     · intro i
-      by_cases hi : ∃ i₀, Fin.castSuccEmb i₀ = i
+      by_cases hi : ∃ i₀, Fin.castSucc i₀ = i
       · obtain ⟨i, rfl⟩ := hi
-        rw [Fin.castSuccEmb.injective.extend_apply]
+        rw [Fin.strictMono_castSucc.injective.extend_apply]
         exact hx i
       · rw [Function.extend_apply' _ _ _ hi, Ne, leadingCoeff_eq_zero, ← card_support_eq_zero, h]
         exact n.succ_ne_zero
-    · rw [Fin.sum_univ_castSuccEmb]
-      simp only [Fin.castSuccEmb.injective.extend_apply]
+    · rw [Fin.sum_univ_castSucc]
+      simp only [Fin.strictMono_castSucc.injective.extend_apply]
       rw [← hf, Function.extend_apply', Function.extend_apply', eraseLead_add_C_mul_X_pow]
       all_goals exact H
 #align polynomial.card_support_eq Polynomial.card_support_eq
@@ -368,7 +368,7 @@ theorem card_support_eq_two :
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h
     refine' ⟨k 0, k 1, hk Nat.zero_lt_one, x 0, x 1, hx 0, hx 1, _⟩
-    rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_one]
+    rw [Fin.sum_univ_castSucc, Fin.sum_univ_one]
     rfl
   · rintro ⟨k, m, hkm, x, y, hx, hy, rfl⟩
     exact card_support_binomial hkm.ne hx hy
@@ -383,7 +383,7 @@ theorem card_support_eq_three :
     refine'
       ⟨k 0, k 1, k 2, hk Nat.zero_lt_one, hk (Nat.lt_succ_self 1), x 0, x 1, x 2, hx 0, hx 1, hx 2,
         _⟩
-    rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_castSuccEmb, Fin.sum_univ_one]
+    rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc, Fin.sum_univ_one]
     rfl
   · rintro ⟨k, m, n, hkm, hmn, x, y, z, hx, hy, hz, rfl⟩
     exact card_support_trinomial hkm hmn hx hy hz

fa256f00

chore: rename Fin.castSucc to Fin.castSuccEmb (#5729)

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

f4e42872

Diff

@@ -315,21 +315,22 @@ theorem card_support_eq {n : ℕ} :
   · exact fun hf => ⟨0, 0, fun x => x.elim0, fun x => x.elim0, card_support_eq_zero.mp hf⟩
   · intro h
     obtain ⟨k, x, hk, hx, hf⟩ := hn (eraseLead_card_support' h)
-    have H : ¬∃ k : Fin n, Fin.castSucc k = Fin.last n := by
+    have H : ¬∃ k : Fin n, Fin.castSuccEmb k = Fin.last n := by
       rintro ⟨i, hi⟩
-      exact i.castSucc_lt_last.ne hi
+      exact i.castSuccEmb_lt_last.ne hi
     refine'
-      ⟨Function.extend Fin.castSucc k fun _ => f.natDegree,
-        Function.extend Fin.castSucc x fun _ => f.leadingCoeff, _, _, _⟩
+      ⟨Function.extend Fin.castSuccEmb k fun _ => f.natDegree,
+        Function.extend Fin.castSuccEmb x fun _ => f.leadingCoeff, _, _, _⟩
     · intro i j hij
-      have hi : i ∈ Set.range (Fin.castSucc : Fin n ↪o Fin (n + 1)) := by
-        rw [Fin.range_castSucc, Set.mem_def]
+      have hi : i ∈ Set.range (Fin.castSuccEmb : Fin n ↪o Fin (n + 1)) := by
+        rw [Fin.range_castSuccEmb, Set.mem_def]
         exact lt_of_lt_of_le hij (Nat.lt_succ_iff.mp j.2)
       obtain ⟨i, rfl⟩ := hi
-      rw [Fin.castSucc.injective.extend_apply]
-      by_cases hj : ∃ j₀, Fin.castSucc j₀ = j
+      rw [Fin.castSuccEmb.injective.extend_apply]
+      by_cases hj : ∃ j₀, Fin.castSuccEmb j₀ = j
       · obtain ⟨j, rfl⟩ := hj
-        rwa [Fin.castSucc.injective.extend_apply, hk.lt_iff_lt, ← Fin.castSucc_lt_castSucc_iff]
+        rwa [Fin.castSuccEmb.injective.extend_apply, hk.lt_iff_lt,
+          ← Fin.castSuccEmb_lt_castSuccEmb_iff]
       · rw [Function.extend_apply' _ _ _ hj]
         apply lt_natDegree_of_mem_eraseLead_support
         rw [mem_support_iff, hf, finset_sum_coeff]
@@ -339,14 +340,14 @@ theorem card_support_eq {n : ℕ} :
           rw [coeff_C_mul, coeff_X_pow, if_neg (hk.injective.ne hji.symm), mul_zero]
         · exact fun hi => (hi (mem_univ i)).elim
     · intro i
-      by_cases hi : ∃ i₀, Fin.castSucc i₀ = i
+      by_cases hi : ∃ i₀, Fin.castSuccEmb i₀ = i
       · obtain ⟨i, rfl⟩ := hi
-        rw [Fin.castSucc.injective.extend_apply]
+        rw [Fin.castSuccEmb.injective.extend_apply]
         exact hx i
       · rw [Function.extend_apply' _ _ _ hi, Ne, leadingCoeff_eq_zero, ← card_support_eq_zero, h]
         exact n.succ_ne_zero
-    · rw [Fin.sum_univ_castSucc]
-      simp only [Fin.castSucc.injective.extend_apply]
+    · rw [Fin.sum_univ_castSuccEmb]
+      simp only [Fin.castSuccEmb.injective.extend_apply]
       rw [← hf, Function.extend_apply', Function.extend_apply', eraseLead_add_C_mul_X_pow]
       all_goals exact H
 #align polynomial.card_support_eq Polynomial.card_support_eq
@@ -367,7 +368,7 @@ theorem card_support_eq_two :
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h
     refine' ⟨k 0, k 1, hk Nat.zero_lt_one, x 0, x 1, hx 0, hx 1, _⟩
-    rw [Fin.sum_univ_castSucc, Fin.sum_univ_one]
+    rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_one]
     rfl
   · rintro ⟨k, m, hkm, x, y, hx, hy, rfl⟩
     exact card_support_binomial hkm.ne hx hy
@@ -382,7 +383,7 @@ theorem card_support_eq_three :
     refine'
       ⟨k 0, k 1, k 2, hk Nat.zero_lt_one, hk (Nat.lt_succ_self 1), x 0, x 1, x 2, hx 0, hx 1, hx 2,
         _⟩
-    rw [Fin.sum_univ_castSucc, Fin.sum_univ_castSucc, Fin.sum_univ_one]
+    rw [Fin.sum_univ_castSuccEmb, Fin.sum_univ_castSuccEmb, Fin.sum_univ_one]
     rfl
   · rintro ⟨k, m, n, hkm, hmn, x, y, z, hx, hy, hz, rfl⟩
     exact card_support_trinomial hkm hmn hx hy hz

fa256f00

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -308,7 +308,7 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
 
 theorem card_support_eq {n : ℕ} :
     f.support.card = n ↔
-      ∃ (k : Fin n → ℕ)(x : Fin n → R)(hk : StrictMono k)(hx : ∀ i, x i ≠ 0),
+      ∃ (k : Fin n → ℕ) (x : Fin n → R) (hk : StrictMono k) (hx : ∀ i, x i ≠ 0),
         f = ∑ i, C (x i) * X ^ k i := by
   refine' ⟨_, fun ⟨k, x, hk, hx, hf⟩ => hf.symm ▸ card_support_eq' k x hk.injective hx⟩
   induction' n with n hn generalizing f
@@ -362,7 +362,8 @@ theorem card_support_eq_one : f.support.card = 1 ↔
 
 theorem card_support_eq_two :
     f.support.card = 2 ↔
-      ∃ (k m : ℕ)(hkm : k < m)(x y : R)(hx : x ≠ 0)(hy : y ≠ 0), f = C x * X ^ k + C y * X ^ m := by
+      ∃ (k m : ℕ) (hkm : k < m) (x y : R) (hx : x ≠ 0) (hy : y ≠ 0),
+        f = C x * X ^ k + C y * X ^ m := by
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h
     refine' ⟨k 0, k 1, hk Nat.zero_lt_one, x 0, x 1, hx 0, hx 1, _⟩
@@ -374,7 +375,7 @@ theorem card_support_eq_two :
 
 theorem card_support_eq_three :
     f.support.card = 3 ↔
-      ∃ (k m n : ℕ)(hkm : k < m)(hmn : m < n)(x y z : R)(hx : x ≠ 0)(hy : y ≠ 0)(hz : z ≠ 0),
+      ∃ (k m n : ℕ) (hkm : k < m) (hmn : m < n) (x y z : R) (hx : x ≠ 0) (hy : y ≠ 0) (hz : z ≠ 0),
         f = C x * X ^ k + C y * X ^ m + C z * X ^ n := by
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, hk, hx, rfl⟩ := card_support_eq.mp h

fa256f00

chore: bye-bye, solo bys! (#3825)

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

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

14167e48

Diff

@@ -315,16 +315,14 @@ theorem card_support_eq {n : ℕ} :
   · exact fun hf => ⟨0, 0, fun x => x.elim0, fun x => x.elim0, card_support_eq_zero.mp hf⟩
   · intro h
     obtain ⟨k, x, hk, hx, hf⟩ := hn (eraseLead_card_support' h)
-    have H : ¬∃ k : Fin n, Fin.castSucc k = Fin.last n :=
-      by
+    have H : ¬∃ k : Fin n, Fin.castSucc k = Fin.last n := by
       rintro ⟨i, hi⟩
       exact i.castSucc_lt_last.ne hi
     refine'
       ⟨Function.extend Fin.castSucc k fun _ => f.natDegree,
         Function.extend Fin.castSucc x fun _ => f.leadingCoeff, _, _, _⟩
     · intro i j hij
-      have hi : i ∈ Set.range (Fin.castSucc : Fin n ↪o Fin (n + 1)) :=
-        by
+      have hi : i ∈ Set.range (Fin.castSucc : Fin n ↪o Fin (n + 1)) := by
         rw [Fin.range_castSucc, Set.mem_def]
         exact lt_of_lt_of_le hij (Nat.lt_succ_iff.mp j.2)
       obtain ⟨i, rfl⟩ := hi
@@ -353,8 +351,8 @@ theorem card_support_eq {n : ℕ} :
       all_goals exact H
 #align polynomial.card_support_eq Polynomial.card_support_eq
 
-theorem card_support_eq_one : f.support.card = 1 ↔ ∃ (k : ℕ)(x : R)(hx : x ≠ 0), f = C x * X ^ k :=
-  by
+theorem card_support_eq_one : f.support.card = 1 ↔
+    ∃ (k : ℕ) (x : R) (hx : x ≠ 0), f = C x * X ^ k := by
   refine' ⟨fun h => _, _⟩
   · obtain ⟨k, x, _, hx, rfl⟩ := card_support_eq.mp h
     exact ⟨k 0, x 0, hx 0, Fin.sum_univ_one _⟩

fa256f00

feat: implement intermediate state for simp_rw (#3738)

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

ff334843

Diff

@@ -296,7 +296,7 @@ theorem card_support_eq' {n : ℕ} (k : Fin n → ℕ) (x : Fin n → R) (hk : F
   suffices (∑ i, C (x i) * X ^ k i).support = image k univ by
     rw [this, univ.card_image_of_injective hk, card_fin]
   simp_rw [Finset.ext_iff, mem_support_iff, finset_sum_coeff, coeff_C_mul_X_pow, mem_image,
-    mem_univ, exists_true_left, true_and]
+    mem_univ, true_and]
   refine' fun i => ⟨fun h => _, _⟩
   · obtain ⟨j, _, h⟩ := exists_ne_zero_of_sum_ne_zero h
     exact ⟨j, (ite_ne_right_iff.mp h).1.symm⟩

fa256f00

feat: improvements to congr! and convert (#2606)

There is now configuration for congr!, convert, and convert_to to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.
congr! now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.
There is now a new HEq congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality ⊢ ⟨a, x⟩ = ⟨b, y⟩ of sigma types, congr! turns this into goals ⊢ a = b and ⊢ a = b → HEq x y (note that congr! will also auto-introduce a = b for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.
congr! (and hence convert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of congr was being abused to unfold definitions.
With set_option trace.congr! true you can see what congr! sees when it is deciding on congruence lemmas.
There is also a bug fix in convert_to to do using 1 when there is no using clause, to match its documentation.

Note that congr! is more capable than congr at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a using clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the typeEqs option), which can help limit the depth automatically.

There is also a predefined configuration that you can invoke with, for example, convert (config := .unfoldSameFun) h, that causes it to behave more like congr, including using default transparency when unfolding.

61ca0ea8

Diff

@@ -230,7 +230,7 @@ theorem induction_with_natDegree_le (P : R[X] → Prop) (N : ℕ) (P_0 : P 0)
   · intro f df f0
     rw [← eraseLead_add_C_mul_X_pow f]
     cases c
-    · convert P_C_mul_pow f.natDegree f.leadingCoeff ?_ df
+    · convert P_C_mul_pow f.natDegree f.leadingCoeff ?_ df using 1
       · convert zero_add (C (leadingCoeff f) * X ^ f.natDegree)
         rw [← card_support_eq_zero, eraseLead_card_support f0]
       · rw [leadingCoeff_ne_zero, Ne.def, ← card_support_eq_zero, f0]

fa256f00

feat: port Data.Polynomial.EraseLead (#2721)

c7d26d40

`data.polynomial.erase_lead` ⟷ `Mathlib.Data.Polynomial.EraseLead`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 8 + 396

data.polynomial.erase_lead ⟷ Mathlib.Data.Polynomial.EraseLead

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 8 + 396

`data.polynomial.erase_lead` ⟷ `Mathlib.Data.Polynomial.EraseLead`

`simp` not firing sometimes