ring_theory.polynomial.eisenstein.basic

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

2032a878

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

814d76e2

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -99,7 +99,7 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo
   by
   rw [aeval_def, Polynomial.eval₂_eq_eval_map, eval_eq_sum_range, range_add_one,
     sum_insert not_mem_range_self, sum_range, (hmo.map (algebraMap R S)).coeff_natDegree,
-    one_mul] at hx 
+    one_mul] at hx
   replace hx := eq_neg_of_add_eq_zero_left hx
   have : ∀ n < f.nat_degree, p ∣ f.coeff n :=
     by
@@ -152,7 +152,7 @@ theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo
   suffices x ^ f.nat_degree ∈ 𝓟 by exact mul_mem_right (x ^ k) 𝓟 this
   rw [is_root.def, eval_eq_sum_range, Finset.range_add_one,
     Finset.sum_insert Finset.not_mem_range_self, Finset.sum_range, hmo.coeff_nat_degree, one_mul] at
-    hroot 
+    hroot
   rw [eq_neg_of_add_eq_zero_left hroot, neg_mem_iff]
   refine' Submodule.sum_mem _ fun i hi => mul_mem_right _ _ (hf.mem (Fin.is_lt i))
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem
@@ -169,7 +169,7 @@ theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f
     obtain ⟨k, hk⟩ := exists_add_of_le hi
     rw [hk, pow_add]
     refine' mul_mem_right _ _ this
-  rw [aeval_def, eval₂_eq_eval_map, ← is_root.def] at hx 
+  rw [aeval_def, eval₂_eq_eval_map, ← is_root.def] at hx
   refine' pow_nat_degree_le_of_root_of_monic_mem (hf.map _) hx (hmo.map _) _ rfl.le
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_aeval_zero_of_monic_mem_map Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map
 -/
@@ -188,7 +188,7 @@ theorem scaleRoots.isWeaklyEisensteinAt (p : R[X]) {x : R} {P : Ideal R} (hP : x
   by
   refine' ⟨fun i hi => _⟩
   rw [coeff_scale_roots]
-  rw [nat_degree_scale_roots, ← tsub_pos_iff_lt] at hi 
+  rw [nat_degree_scale_roots, ← tsub_pos_iff_lt] at hi
   exact Ideal.mul_mem_left _ _ (Ideal.pow_mem_of_mem P hP _ hi)
 #align polynomial.scale_roots.is_weakly_eisenstein_at Polynomial.scaleRoots.isWeaklyEisensteinAt
 -/
@@ -203,9 +203,9 @@ theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Inje
     (scale_roots.is_weakly_eisenstein_at _
           (ideal.mem_span_singleton.mpr <| dvd_refl x)).pow_natDegree_le_of_root_of_monic_mem
       _ ((monic_scale_roots_iff x).mpr hp) _ le_rfl
-  rw [injective_iff_map_eq_zero'] at hf 
+  rw [injective_iff_map_eq_zero'] at hf
   have := scale_roots_eval₂_eq_zero f h
-  rwa [hz, Polynomial.eval₂_at_apply, hf] at this 
+  rwa [hz, Polynomial.eval₂_at_apply, hf] at this
 #align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero
 -/

814d76e2

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) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Mathbin.RingTheory.EisensteinCriterion
-import Mathbin.RingTheory.Polynomial.ScaleRoots
+import RingTheory.EisensteinCriterion
+import RingTheory.Polynomial.ScaleRoots
 
 #align_import ring_theory.polynomial.eisenstein.basic from "leanprover-community/mathlib"@"814d76e2247d5ba8bc024843552da1278bfe9e5c"

814d76e2

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) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.eisenstein.basic
-! leanprover-community/mathlib commit 814d76e2247d5ba8bc024843552da1278bfe9e5c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.EisensteinCriterion
 import Mathbin.RingTheory.Polynomial.ScaleRoots
 
+#align_import ring_theory.polynomial.eisenstein.basic from "leanprover-community/mathlib"@"814d76e2247d5ba8bc024843552da1278bfe9e5c"
+
 /-!
 # Eisenstein polynomials

814d76e2

bump to nightly-2023-06-21-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9

78c41114

Diff

@@ -229,21 +229,20 @@ section CommSemiring
 
 variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsEisensteinAt 𝓟)
 
-#print Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem /-
-theorem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤) :
-    ¬f.leadingCoeff ∈ 𝓟 :=
+#print Polynomial.Monic.leadingCoeff_not_mem /-
+theorem Polynomial.Monic.leadingCoeff_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤) : ¬f.leadingCoeff ∈ 𝓟 :=
   hf.leadingCoeff.symm ▸ (Ideal.ne_top_iff_one _).1 h
-#align polynomial.monic.leading_coeff_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem
+#align polynomial.monic.leading_coeff_not_mem Polynomial.Monic.leadingCoeff_not_mem
 -/
 
-#print Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem /-
-theorem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem (hf : f.Monic)
-    (h : 𝓟 ≠ ⊤) (hmem : ∀ {n}, n < f.natDegree → f.coeff n ∈ 𝓟) (hnot_mem : f.coeff 0 ∉ 𝓟 ^ 2) :
+#print Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem /-
+theorem Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤)
+    (hmem : ∀ {n}, n < f.natDegree → f.coeff n ∈ 𝓟) (hnot_mem : f.coeff 0 ∉ 𝓟 ^ 2) :
     f.IsEisensteinAt 𝓟 :=
   { leading := hf.leadingCoeff_not_mem h
     Mem := fun n hn => hmem hn
     not_mem := hnot_mem }
-#align polynomial.monic.is_eisenstein_at_of_mem_of_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem
+#align polynomial.monic.is_eisenstein_at_of_mem_of_not_mem Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem
 -/
 
 #print Polynomial.IsEisensteinAt.isWeaklyEisensteinAt /-

814d76e2

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -72,14 +72,14 @@ section CommSemiring
 
 variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsWeaklyEisensteinAt 𝓟)
 
-include hf
-
+#print Polynomial.IsWeaklyEisensteinAt.map /-
 theorem map {A : Type v} [CommRing A] (φ : R →+* A) : (f.map φ).IsWeaklyEisensteinAt (𝓟.map φ) :=
   by
   refine' (is_weakly_eisenstein_at_iff _ _).2 fun n hn => _
   rw [coeff_map]
   exact mem_map_of_mem _ (hf.mem (lt_of_lt_of_le hn (nat_degree_map_le _ _)))
 #align polynomial.is_weakly_eisenstein_at.map Polynomial.IsWeaklyEisensteinAt.map
+-/
 
 end CommSemiring
 
@@ -93,9 +93,9 @@ section Principal
 
 variable {p : R}
 
--- mathport name: exprP
 local notation "P" => Submodule.span R {p}
 
+#print Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree /-
 theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo : f.Monic)
     (hf : f.IsWeaklyEisensteinAt P) :
     ∃ y ∈ adjoin R ({x} : Set S), (algebraMap R S) p * y = x ^ (f.map (algebraMap R S)).natDegree :=
@@ -125,7 +125,9 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo
         Subalgebra.mul_mem _ (Subalgebra.algebraMap_mem _ _)
           (Subalgebra.pow_mem _ (subset_adjoin (Set.mem_singleton x)) _))
 #align polynomial.is_weakly_eisenstein_at.exists_mem_adjoin_mul_eq_pow_nat_degree Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree
+-/
 
+#print Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le /-
 theorem exists_mem_adjoin_mul_eq_pow_natDegree_le {x : S} (hx : aeval x f = 0) (hmo : f.Monic)
     (hf : f.IsWeaklyEisensteinAt P) :
     ∀ i,
@@ -140,11 +142,11 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree_le {x : S} (hx : aeval x f = 0) (
   · exact Subalgebra.mul_mem _ hy (Subalgebra.pow_mem _ (subset_adjoin (Set.mem_singleton x)) _)
   · rw [← mul_assoc _ y, H]
 #align polynomial.is_weakly_eisenstein_at.exists_mem_adjoin_mul_eq_pow_nat_degree_le Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le
+-/
 
 end Principal
 
-include hf
-
+#print Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem /-
 theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo : f.Monic) :
     ∀ i, f.natDegree ≤ i → x ^ i ∈ 𝓟 := by
   intro i hi
@@ -157,7 +159,9 @@ theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo
   rw [eq_neg_of_add_eq_zero_left hroot, neg_mem_iff]
   refine' Submodule.sum_mem _ fun i hi => mul_mem_right _ _ (hf.mem (Fin.is_lt i))
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem
+-/
 
+#print Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map /-
 theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f = 0)
     (hmo : f.Monic) :
     ∀ i, (f.map (algebraMap R S)).natDegree ≤ i → x ^ i ∈ 𝓟.map (algebraMap R S) :=
@@ -171,6 +175,7 @@ theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f
   rw [aeval_def, eval₂_eq_eval_map, ← is_root.def] at hx 
   refine' pow_nat_degree_le_of_root_of_monic_mem (hf.map _) hx (hmo.map _) _ rfl.le
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_aeval_zero_of_monic_mem_map Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map
+-/
 
 end CommRing
 
@@ -191,6 +196,7 @@ theorem scaleRoots.isWeaklyEisensteinAt (p : R[X]) {x : R} {P : Ideal R} (hP : x
 #align polynomial.scale_roots.is_weakly_eisenstein_at Polynomial.scaleRoots.isWeaklyEisensteinAt
 -/
 
+#print Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero /-
 theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Injective f) {p : R[X]}
     (hp : p.Monic) (x y : R) (z : A) (h : p.eval₂ f z = 0) (hz : f x * z = f y) :
     x ∣ y ^ p.natDegree :=
@@ -204,13 +210,16 @@ theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Inje
   have := scale_roots_eval₂_eq_zero f h
   rwa [hz, Polynomial.eval₂_at_apply, hf] at this 
 #align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero
+-/
 
+#print Polynomial.dvd_pow_natDegree_of_aeval_eq_zero /-
 theorem dvd_pow_natDegree_of_aeval_eq_zero [Algebra R A] [Nontrivial A] [NoZeroSMulDivisors R A]
     {p : R[X]} (hp : p.Monic) (x y : R) (z : A) (h : Polynomial.aeval z p = 0)
     (hz : z * algebraMap R A x = algebraMap R A y) : x ∣ y ^ p.natDegree :=
   dvd_pow_natDegree_of_eval₂_eq_zero (NoZeroSMulDivisors.algebraMap_injective R A) hp x y z h
     ((mul_comm _ _).trans hz)
 #align polynomial.dvd_pow_nat_degree_of_aeval_eq_zero Polynomial.dvd_pow_natDegree_of_aeval_eq_zero
+-/
 
 end ScaleRoots
 
@@ -220,11 +229,14 @@ section CommSemiring
 
 variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsEisensteinAt 𝓟)
 
+#print Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem /-
 theorem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤) :
     ¬f.leadingCoeff ∈ 𝓟 :=
   hf.leadingCoeff.symm ▸ (Ideal.ne_top_iff_one _).1 h
 #align polynomial.monic.leading_coeff_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem
+-/
 
+#print Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem /-
 theorem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem (hf : f.Monic)
     (h : 𝓟 ≠ ⊤) (hmem : ∀ {n}, n < f.natDegree → f.coeff n ∈ 𝓟) (hnot_mem : f.coeff 0 ∉ 𝓟 ^ 2) :
     f.IsEisensteinAt 𝓟 :=
@@ -232,8 +244,7 @@ theorem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_
     Mem := fun n hn => hmem hn
     not_mem := hnot_mem }
 #align polynomial.monic.is_eisenstein_at_of_mem_of_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem
-
-include hf
+-/
 
 #print Polynomial.IsEisensteinAt.isWeaklyEisensteinAt /-
 theorem isWeaklyEisensteinAt : IsWeaklyEisensteinAt f 𝓟 :=
@@ -257,6 +268,7 @@ section IsDomain
 
 variable [CommRing R] [IsDomain R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsEisensteinAt 𝓟)
 
+#print Polynomial.IsEisensteinAt.irreducible /-
 /-- If a primitive `f` satisfies `f.is_eisenstein_at 𝓟`, where `𝓟.is_prime`, then `f` is
 irreducible. -/
 theorem irreducible (hprime : 𝓟.IsPrime) (hu : f.IsPrimitive) (hfd0 : 0 < f.natDegree) :
@@ -264,6 +276,7 @@ theorem irreducible (hprime : 𝓟.IsPrime) (hu : f.IsPrimitive) (hfd0 : 0 < f.n
   irreducible_of_eisenstein_criterion hprime hf.leading (fun n hn => hf.Mem (coe_lt_degree.1 hn))
     (natDegree_pos_iff_degree_pos.1 hfd0) hf.not_mem hu
 #align polynomial.is_eisenstein_at.irreducible Polynomial.IsEisensteinAt.irreducible
+-/
 
 end IsDomain

814d76e2

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -102,7 +102,7 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo
   by
   rw [aeval_def, Polynomial.eval₂_eq_eval_map, eval_eq_sum_range, range_add_one,
     sum_insert not_mem_range_self, sum_range, (hmo.map (algebraMap R S)).coeff_natDegree,
-    one_mul] at hx
+    one_mul] at hx 
   replace hx := eq_neg_of_add_eq_zero_left hx
   have : ∀ n < f.nat_degree, p ∣ f.coeff n :=
     by
@@ -153,7 +153,7 @@ theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo
   suffices x ^ f.nat_degree ∈ 𝓟 by exact mul_mem_right (x ^ k) 𝓟 this
   rw [is_root.def, eval_eq_sum_range, Finset.range_add_one,
     Finset.sum_insert Finset.not_mem_range_self, Finset.sum_range, hmo.coeff_nat_degree, one_mul] at
-    hroot
+    hroot 
   rw [eq_neg_of_add_eq_zero_left hroot, neg_mem_iff]
   refine' Submodule.sum_mem _ fun i hi => mul_mem_right _ _ (hf.mem (Fin.is_lt i))
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem
@@ -168,7 +168,7 @@ theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f
     obtain ⟨k, hk⟩ := exists_add_of_le hi
     rw [hk, pow_add]
     refine' mul_mem_right _ _ this
-  rw [aeval_def, eval₂_eq_eval_map, ← is_root.def] at hx
+  rw [aeval_def, eval₂_eq_eval_map, ← is_root.def] at hx 
   refine' pow_nat_degree_le_of_root_of_monic_mem (hf.map _) hx (hmo.map _) _ rfl.le
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_aeval_zero_of_monic_mem_map Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map
 
@@ -186,7 +186,7 @@ theorem scaleRoots.isWeaklyEisensteinAt (p : R[X]) {x : R} {P : Ideal R} (hP : x
   by
   refine' ⟨fun i hi => _⟩
   rw [coeff_scale_roots]
-  rw [nat_degree_scale_roots, ← tsub_pos_iff_lt] at hi
+  rw [nat_degree_scale_roots, ← tsub_pos_iff_lt] at hi 
   exact Ideal.mul_mem_left _ _ (Ideal.pow_mem_of_mem P hP _ hi)
 #align polynomial.scale_roots.is_weakly_eisenstein_at Polynomial.scaleRoots.isWeaklyEisensteinAt
 -/
@@ -200,9 +200,9 @@ theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Inje
     (scale_roots.is_weakly_eisenstein_at _
           (ideal.mem_span_singleton.mpr <| dvd_refl x)).pow_natDegree_le_of_root_of_monic_mem
       _ ((monic_scale_roots_iff x).mpr hp) _ le_rfl
-  rw [injective_iff_map_eq_zero'] at hf
+  rw [injective_iff_map_eq_zero'] at hf 
   have := scale_roots_eval₂_eq_zero f h
-  rwa [hz, Polynomial.eval₂_at_apply, hf] at this
+  rwa [hz, Polynomial.eval₂_at_apply, hf] at this 
 #align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero
 
 theorem dvd_pow_natDegree_of_aeval_eq_zero [Algebra R A] [Nontrivial A] [NoZeroSMulDivisors R A]

814d76e2

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -96,7 +96,6 @@ variable {p : R}
 -- mathport name: exprP
 local notation "P" => Submodule.span R {p}
 
-#print Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree /-
 theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo : f.Monic)
     (hf : f.IsWeaklyEisensteinAt P) :
     ∃ y ∈ adjoin R ({x} : Set S), (algebraMap R S) p * y = x ^ (f.map (algebraMap R S)).natDegree :=
@@ -115,7 +114,7 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo
     congr
     skip
     ext
-    rw [[anonymous], coeff_map, hφ i.1 (lt_of_lt_of_le i.2 (nat_degree_map_le _ _)),
+    rw [Fin.coe_eq_val, coeff_map, hφ i.1 (lt_of_lt_of_le i.2 (nat_degree_map_le _ _)),
       RingHom.map_mul, mul_assoc]
   rw [hx, ← mul_sum, neg_eq_neg_one_mul, ← mul_assoc (-1 : S), mul_comm (-1 : S), mul_assoc]
   refine'
@@ -126,9 +125,7 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo
         Subalgebra.mul_mem _ (Subalgebra.algebraMap_mem _ _)
           (Subalgebra.pow_mem _ (subset_adjoin (Set.mem_singleton x)) _))
 #align polynomial.is_weakly_eisenstein_at.exists_mem_adjoin_mul_eq_pow_nat_degree Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree
--/
 
-#print Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le /-
 theorem exists_mem_adjoin_mul_eq_pow_natDegree_le {x : S} (hx : aeval x f = 0) (hmo : f.Monic)
     (hf : f.IsWeaklyEisensteinAt P) :
     ∀ i,
@@ -143,7 +140,6 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree_le {x : S} (hx : aeval x f = 0) (
   · exact Subalgebra.mul_mem _ hy (Subalgebra.pow_mem _ (subset_adjoin (Set.mem_singleton x)) _)
   · rw [← mul_assoc _ y, H]
 #align polynomial.is_weakly_eisenstein_at.exists_mem_adjoin_mul_eq_pow_nat_degree_le Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le
--/
 
 end Principal
 
@@ -162,7 +158,6 @@ theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo
   refine' Submodule.sum_mem _ fun i hi => mul_mem_right _ _ (hf.mem (Fin.is_lt i))
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem
 
-#print Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map /-
 theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f = 0)
     (hmo : f.Monic) :
     ∀ i, (f.map (algebraMap R S)).natDegree ≤ i → x ^ i ∈ 𝓟.map (algebraMap R S) :=
@@ -176,7 +171,6 @@ theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f
   rw [aeval_def, eval₂_eq_eval_map, ← is_root.def] at hx
   refine' pow_nat_degree_le_of_root_of_monic_mem (hf.map _) hx (hmo.map _) _ rfl.le
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_aeval_zero_of_monic_mem_map Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map
--/
 
 end CommRing

814d76e2

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -41,7 +41,7 @@ variable {R : Type u}
 
 open Ideal Algebra Finset
 
-open BigOperators Polynomial
+open scoped BigOperators Polynomial
 
 namespace Polynomial

814d76e2

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -74,12 +74,6 @@ variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsWeaklyEisenstein
 
 include hf
 
-/- warning: polynomial.is_weakly_eisenstein_at.map -> Polynomial.IsWeaklyEisensteinAt.map is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsWeaklyEisensteinAt.{u1} R _inst_1 f 𝓟) -> (forall {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] (φ : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))), Polynomial.IsWeaklyEisensteinAt.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) (Polynomial.map.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) φ f) (Ideal.map.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.ringHomClass.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) φ 𝓟))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsWeaklyEisensteinAt.{u1} R _inst_1 f 𝓟) -> (forall {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] (φ : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))), Polynomial.IsWeaklyEisensteinAt.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) (Polynomial.map.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) φ f) (Ideal.map.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) φ 𝓟))
-Case conversion may be inaccurate. Consider using '#align polynomial.is_weakly_eisenstein_at.map Polynomial.IsWeaklyEisensteinAt.mapₓ'. -/
 theorem map {A : Type v} [CommRing A] (φ : R →+* A) : (f.map φ).IsWeaklyEisensteinAt (𝓟.map φ) :=
   by
   refine' (is_weakly_eisenstein_at_iff _ _).2 fun n hn => _
@@ -155,12 +149,6 @@ end Principal
 
 include hf
 
-/- warning: polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem -> Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem is a dubious translation:
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-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {𝓟 : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.IsWeaklyEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f x) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) -> (forall (i : Nat), (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) i) -> (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x i) 𝓟)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Polynomial.IsWeaklyEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f x) -> (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f) -> (forall (i : Nat), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f) i) -> (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x i) 𝓟)))
-Case conversion may be inaccurate. Consider using '#align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_memₓ'. -/
 theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo : f.Monic) :
     ∀ i, f.natDegree ≤ i → x ^ i ∈ 𝓟 := by
   intro i hi
@@ -209,9 +197,6 @@ theorem scaleRoots.isWeaklyEisensteinAt (p : R[X]) {x : R} {P : Ideal R} (hP : x
 #align polynomial.scale_roots.is_weakly_eisenstein_at Polynomial.scaleRoots.isWeaklyEisensteinAt
 -/
 
-/- warning: polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero -> Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Injective f) {p : R[X]}
     (hp : p.Monic) (x y : R) (z : A) (h : p.eval₂ f z = 0) (hz : f x * z = f y) :
     x ∣ y ^ p.natDegree :=
@@ -226,9 +211,6 @@ theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Inje
   rwa [hz, Polynomial.eval₂_at_apply, hf] at this
 #align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero
 
-/- warning: polynomial.dvd_pow_nat_degree_of_aeval_eq_zero -> Polynomial.dvd_pow_natDegree_of_aeval_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_aeval_eq_zero Polynomial.dvd_pow_natDegree_of_aeval_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_aeval_eq_zero [Algebra R A] [Nontrivial A] [NoZeroSMulDivisors R A]
     {p : R[X]} (hp : p.Monic) (x y : R) (z : A) (h : Polynomial.aeval z p = 0)
     (hz : z * algebraMap R A x = algebraMap R A y) : x ∣ y ^ p.natDegree :=
@@ -244,23 +226,11 @@ section CommSemiring
 
 variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsEisensteinAt 𝓟)
 
-/- warning: polynomial.monic.leading_coeff_not_mem -> Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 𝓟 (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) -> (Not (Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) 𝓟))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 𝓟 (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) -> (Not (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) 𝓟))
-Case conversion may be inaccurate. Consider using '#align polynomial.monic.leading_coeff_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_memₓ'. -/
 theorem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤) :
     ¬f.leadingCoeff ∈ 𝓟 :=
   hf.leadingCoeff.symm ▸ (Ideal.ne_top_iff_one _).1 h
 #align polynomial.monic.leading_coeff_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem
 
-/- warning: polynomial.monic.is_eisenstein_at_of_mem_of_not_mem -> Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem is a dubious translation:
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 theorem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem (hf : f.Monic)
     (h : 𝓟 ≠ ⊤) (hmem : ∀ {n}, n < f.natDegree → f.coeff n ∈ 𝓟) (hnot_mem : f.coeff 0 ∉ 𝓟 ^ 2) :
     f.IsEisensteinAt 𝓟 :=
@@ -293,12 +263,6 @@ section IsDomain
 
 variable [CommRing R] [IsDomain R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsEisensteinAt 𝓟)
 
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 /-- If a primitive `f` satisfies `f.is_eisenstein_at 𝓟`, where `𝓟.is_prime`, then `f` is
 irreducible. -/
 theorem irreducible (hprime : 𝓟.IsPrime) (hu : f.IsPrimitive) (hfd0 : 0 < f.natDegree) :

814d76e2

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -210,10 +210,7 @@ theorem scaleRoots.isWeaklyEisensteinAt (p : R[X]) {x : R} {P : Ideal R} (hP : x
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Injective f) {p : R[X]}
     (hp : p.Monic) (x y : R) (z : A) (h : p.eval₂ f z = 0) (hz : f x * z = f y) :
@@ -230,10 +227,7 @@ theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Inje
 #align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero
 
 /- warning: polynomial.dvd_pow_nat_degree_of_aeval_eq_zero -> Polynomial.dvd_pow_natDegree_of_aeval_eq_zero is a dubious translation:
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-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Nontrivial.{u1} A] [_inst_5 : NoZeroSMulDivisors.{u2, u1} R A (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)] {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} ((fun 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3))))) (Polynomial.aeval.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) _inst_2)))))) -> (Eq.{succ u1} A (HMul.hMul.{u1, u1, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) A (instHMul.{u1} A (NonUnitalNonAssocRing.toMul.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_aeval_eq_zero Polynomial.dvd_pow_natDegree_of_aeval_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_aeval_eq_zero [Algebra R A] [Nontrivial A] [NoZeroSMulDivisors R A]
     {p : R[X]} (hp : p.Monic) (x y : R) (z : A) (h : Polynomial.aeval z p = 0)

814d76e2

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -233,7 +233,7 @@ theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Inje
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_4 : Nontrivial.{u2} A] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3)))))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) A (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3) (Polynomial.aeval.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A (CommRing.toRing.{u2} A _inst_2)))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) y)) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Nontrivial.{u1} A] [_inst_5 : NoZeroSMulDivisors.{u2, u1} R A (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)] {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3 (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3))))) (Polynomial.aeval.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p))))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Nontrivial.{u1} A] [_inst_5 : NoZeroSMulDivisors.{u2, u1} R A (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)] {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) 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(CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_aeval_eq_zero Polynomial.dvd_pow_natDegree_of_aeval_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_aeval_eq_zero [Algebra R A] [Nontrivial A] [NoZeroSMulDivisors R A]
     {p : R[X]} (hp : p.Monic) (x y : R) (z : A) (h : Polynomial.aeval z p = 0)

814d76e2

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -213,7 +213,7 @@ theorem scaleRoots.isWeaklyEisensteinAt (p : R[X]) {x : R} {P : Ideal R} (hP : x
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] {f : RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))}, (Function.Injective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) f)) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u2} A (Polynomial.eval₂.{u1, u2} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) f z p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) f x) z) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) f y)) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] {f : RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))}, (Function.Injective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) f)) -> (forall {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} A (Polynomial.eval₂.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) f z p) (OfNat.ofNat.{u1} A 0 (Zero.toOfNat0.{u1} A (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) f x) z) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) f y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p)))))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] {f : RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))}, (Function.Injective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) f)) -> (forall {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} A (Polynomial.eval₂.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) f z p) (OfNat.ofNat.{u1} A 0 (Zero.toOfNat0.{u1} A (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) x) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) f x) z) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) f y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Injective f) {p : R[X]}
     (hp : p.Monic) (x y : R) (z : A) (h : p.eval₂ f z = 0) (hz : f x * z = f y) :
@@ -233,7 +233,7 @@ theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Inje
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_4 : Nontrivial.{u2} A] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3)))))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) A (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) A (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) A (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3) (Polynomial.aeval.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A (CommRing.toRing.{u2} A _inst_2)))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) y)) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Nontrivial.{u1} A] [_inst_5 : NoZeroSMulDivisors.{u2, u1} R A (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)] {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R 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(Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3 (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3))))) (Polynomial.aeval.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p))))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Nontrivial.{u1} A] [_inst_5 : NoZeroSMulDivisors.{u2, u1} R A (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)] {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) 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(CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3 (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3))))) (Polynomial.aeval.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R 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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_aeval_eq_zero Polynomial.dvd_pow_natDegree_of_aeval_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_aeval_eq_zero [Algebra R A] [Nontrivial A] [NoZeroSMulDivisors R A]
     {p : R[X]} (hp : p.Monic) (x y : R) (z : A) (h : Polynomial.aeval z p = 0)

814d76e2

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -78,7 +78,7 @@ include hf
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsWeaklyEisensteinAt.{u1} R _inst_1 f 𝓟) -> (forall {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] (φ : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))), Polynomial.IsWeaklyEisensteinAt.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) (Polynomial.map.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) φ f) (Ideal.map.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.ringHomClass.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) φ 𝓟))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsWeaklyEisensteinAt.{u1} R _inst_1 f 𝓟) -> (forall {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] (φ : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))), Polynomial.IsWeaklyEisensteinAt.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) (Polynomial.map.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) φ f) (Ideal.map.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) φ 𝓟))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsWeaklyEisensteinAt.{u1} R _inst_1 f 𝓟) -> (forall {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] (φ : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))), Polynomial.IsWeaklyEisensteinAt.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) (Polynomial.map.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) φ f) (Ideal.map.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) φ 𝓟))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_weakly_eisenstein_at.map Polynomial.IsWeaklyEisensteinAt.mapₓ'. -/
 theorem map {A : Type v} [CommRing A] (φ : R →+* A) : (f.map φ).IsWeaklyEisensteinAt (𝓟.map φ) :=
   by
@@ -159,7 +159,7 @@ include hf
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {𝓟 : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.IsWeaklyEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f x) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) -> (forall (i : Nat), (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) i) -> (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x i) 𝓟)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {𝓟 : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.IsWeaklyEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f x) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) -> (forall (i : Nat), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) i) -> (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x i) 𝓟)))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Polynomial.IsWeaklyEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f x) -> (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f) -> (forall (i : Nat), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f) i) -> (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) x i) 𝓟)))
 Case conversion may be inaccurate. Consider using '#align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_memₓ'. -/
 theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo : f.Monic) :
     ∀ i, f.natDegree ≤ i → x ^ i ∈ 𝓟 := by
@@ -213,7 +213,7 @@ theorem scaleRoots.isWeaklyEisensteinAt (p : R[X]) {x : R} {P : Ideal R} (hP : x
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] {f : RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))}, (Function.Injective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) f)) -> (forall {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u2} A (Polynomial.eval₂.{u1, u2} R A (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) f z p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) f x) z) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) f y)) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p)))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] {f : RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))}, (Function.Injective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))))) f)) -> (forall {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} A (Polynomial.eval₂.{u2, u1} R A (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) f z p) (OfNat.ofNat.{u1} A 0 (Zero.toOfNat0.{u1} A (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))))) f x) z) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))))) f y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) p)))))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] {f : RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))}, (Function.Injective.{succ u2, succ u1} R A (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) f)) -> (forall {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} A (Polynomial.eval₂.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) f z p) (OfNat.ofNat.{u1} A 0 (Zero.toOfNat0.{u1} A (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) _inst_2))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) f x) z) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) f y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Injective f) {p : R[X]}
     (hp : p.Monic) (x y : R) (z : A) (h : p.eval₂ f z = 0) (hz : f x * z = f y) :
@@ -233,7 +233,7 @@ theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Inje
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_4 : Nontrivial.{u2} A] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3)))))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R 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(Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) A (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3) (Polynomial.aeval.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A (CommRing.toRing.{u2} A _inst_2)))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) y)) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))] [_inst_4 : Nontrivial.{u1} A] [_inst_5 : NoZeroSMulDivisors.{u2, u1} R A (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3)] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3 (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3))))) (Polynomial.aeval.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) _inst_2)))))) -> (Eq.{succ u1} A (HMul.hMul.{u1, u1, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) A (instHMul.{u1} A (NonUnitalNonAssocRing.toMul.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3) y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) p))))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_4 : Nontrivial.{u1} A] [_inst_5 : NoZeroSMulDivisors.{u2, u1} R A (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)] {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3 (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3))))) (Polynomial.aeval.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) _inst_2)))))) -> (Eq.{succ u1} A (HMul.hMul.{u1, u1, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) A (instHMul.{u1} A (NonUnitalNonAssocRing.toMul.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)))) R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_3) y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) p))))
 Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_aeval_eq_zero Polynomial.dvd_pow_natDegree_of_aeval_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_aeval_eq_zero [Algebra R A] [Nontrivial A] [NoZeroSMulDivisors R A]
     {p : R[X]} (hp : p.Monic) (x y : R) (z : A) (h : Polynomial.aeval z p = 0)
@@ -303,7 +303,7 @@ variable [CommRing R] [IsDomain R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsEisenst
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {𝓟 : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.IsEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 𝓟) -> (Polynomial.IsPrimitive.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f) -> (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f)) -> (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {𝓟 : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.IsEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 𝓟) -> (Polynomial.IsPrimitive.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f)) -> (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))}, (Polynomial.IsEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (Ideal.IsPrime.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 𝓟) -> (Polynomial.IsPrimitive.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) f)) -> (Irreducible.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) f)
 Case conversion may be inaccurate. Consider using '#align polynomial.is_eisenstein_at.irreducible Polynomial.IsEisensteinAt.irreducibleₓ'. -/
 /-- If a primitive `f` satisfies `f.is_eisenstein_at 𝓟`, where `𝓟.is_prime`, then `f` is
 irreducible. -/

814d76e2

bump to nightly-2023-04-13-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

bd75793a

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.eisenstein.basic
-! leanprover-community/mathlib commit 2032a878972d5672e7c27c957e7a6e297b044973
+! leanprover-community/mathlib commit 814d76e2247d5ba8bc024843552da1278bfe9e5c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.RingTheory.Polynomial.ScaleRoots
 
 /-!
 # Eisenstein polynomials
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 Given an ideal `𝓟` of a commutative semiring `R`, we say that a polynomial `f : R[X]` is
 *Eisenstein at `𝓟`* if `f.leading_coeff ∉ 𝓟`, `∀ n, n < f.nat_degree → f.coeff n ∈ 𝓟` and
 `f.coeff 0 ∉ 𝓟 ^ 2`. In this file we gather miscellaneous results about Eisenstein polynomials.

2032a878

bump to nightly-2023-04-11-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/c9236f47f5b9df573443aa499c0d3968769628b7

b17cb689

Diff

@@ -42,13 +42,16 @@ open BigOperators Polynomial
 
 namespace Polynomial
 
+#print Polynomial.IsWeaklyEisensteinAt /-
 /-- Given an ideal `𝓟` of a commutative semiring `R`, we say that a polynomial `f : R[X]`
 is *weakly Eisenstein at `𝓟`* if `∀ n, n < f.nat_degree → f.coeff n ∈ 𝓟`. -/
 @[mk_iff]
 structure IsWeaklyEisensteinAt [CommSemiring R] (f : R[X]) (𝓟 : Ideal R) : Prop where
   Mem : ∀ {n}, n < f.natDegree → f.coeff n ∈ 𝓟
 #align polynomial.is_weakly_eisenstein_at Polynomial.IsWeaklyEisensteinAt
+-/
 
+#print Polynomial.IsEisensteinAt /-
 /-- Given an ideal `𝓟` of a commutative semiring `R`, we say that a polynomial `f : R[X]`
 is *Eisenstein at `𝓟`* if `f.leading_coeff ∉ 𝓟`, `∀ n, n < f.nat_degree → f.coeff n ∈ 𝓟` and
 `f.coeff 0 ∉ 𝓟 ^ 2`. -/
@@ -58,6 +61,7 @@ structure IsEisensteinAt [CommSemiring R] (f : R[X]) (𝓟 : Ideal R) : Prop whe
   Mem : ∀ {n}, n < f.natDegree → f.coeff n ∈ 𝓟
   not_mem : f.coeff 0 ∉ 𝓟 ^ 2
 #align polynomial.is_eisenstein_at Polynomial.IsEisensteinAt
+-/
 
 namespace IsWeaklyEisensteinAt
 
@@ -67,6 +71,12 @@ variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsWeaklyEisenstein
 
 include hf
 
+/- warning: polynomial.is_weakly_eisenstein_at.map -> Polynomial.IsWeaklyEisensteinAt.map is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsWeaklyEisensteinAt.{u1} R _inst_1 f 𝓟) -> (forall {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] (φ : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))), Polynomial.IsWeaklyEisensteinAt.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) (Polynomial.map.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) φ f) (Ideal.map.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.ringHomClass.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) φ 𝓟))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.IsWeaklyEisensteinAt.{u1} R _inst_1 f 𝓟) -> (forall {A : Type.{u2}} [_inst_2 : CommRing.{u2} A] (φ : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))), Polynomial.IsWeaklyEisensteinAt.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2) (Polynomial.map.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) φ f) (Ideal.map.{u1, u2, max u1 u2} R A (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))) φ 𝓟))
+Case conversion may be inaccurate. Consider using '#align polynomial.is_weakly_eisenstein_at.map Polynomial.IsWeaklyEisensteinAt.mapₓ'. -/
 theorem map {A : Type v} [CommRing A] (φ : R →+* A) : (f.map φ).IsWeaklyEisensteinAt (𝓟.map φ) :=
   by
   refine' (is_weakly_eisenstein_at_iff _ _).2 fun n hn => _
@@ -89,6 +99,7 @@ variable {p : R}
 -- mathport name: exprP
 local notation "P" => Submodule.span R {p}
 
+#print Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree /-
 theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo : f.Monic)
     (hf : f.IsWeaklyEisensteinAt P) :
     ∃ y ∈ adjoin R ({x} : Set S), (algebraMap R S) p * y = x ^ (f.map (algebraMap R S)).natDegree :=
@@ -118,7 +129,9 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo
         Subalgebra.mul_mem _ (Subalgebra.algebraMap_mem _ _)
           (Subalgebra.pow_mem _ (subset_adjoin (Set.mem_singleton x)) _))
 #align polynomial.is_weakly_eisenstein_at.exists_mem_adjoin_mul_eq_pow_nat_degree Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree
+-/
 
+#print Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le /-
 theorem exists_mem_adjoin_mul_eq_pow_natDegree_le {x : S} (hx : aeval x f = 0) (hmo : f.Monic)
     (hf : f.IsWeaklyEisensteinAt P) :
     ∀ i,
@@ -133,11 +146,18 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree_le {x : S} (hx : aeval x f = 0) (
   · exact Subalgebra.mul_mem _ hy (Subalgebra.pow_mem _ (subset_adjoin (Set.mem_singleton x)) _)
   · rw [← mul_assoc _ y, H]
 #align polynomial.is_weakly_eisenstein_at.exists_mem_adjoin_mul_eq_pow_nat_degree_le Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le
+-/
 
 end Principal
 
 include hf
 
+/- warning: polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem -> Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {𝓟 : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.IsWeaklyEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f x) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) -> (forall (i : Nat), (LE.le.{0} Nat Nat.hasLe (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) i) -> (Membership.Mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) x i) 𝓟)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {𝓟 : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.IsWeaklyEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (forall {x : R}, (Polynomial.IsRoot.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f x) -> (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) -> (forall (i : Nat), (LE.le.{0} Nat instLENat (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f) i) -> (Membership.mem.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) R (Submodule.setLike.{u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) x i) 𝓟)))
+Case conversion may be inaccurate. Consider using '#align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_memₓ'. -/
 theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo : f.Monic) :
     ∀ i, f.natDegree ≤ i → x ^ i ∈ 𝓟 := by
   intro i hi
@@ -151,6 +171,7 @@ theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo
   refine' Submodule.sum_mem _ fun i hi => mul_mem_right _ _ (hf.mem (Fin.is_lt i))
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem
 
+#print Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map /-
 theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f = 0)
     (hmo : f.Monic) :
     ∀ i, (f.map (algebraMap R S)).natDegree ≤ i → x ^ i ∈ 𝓟.map (algebraMap R S) :=
@@ -164,6 +185,7 @@ theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f
   rw [aeval_def, eval₂_eq_eval_map, ← is_root.def] at hx
   refine' pow_nat_degree_le_of_root_of_monic_mem (hf.map _) hx (hmo.map _) _ rfl.le
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_aeval_zero_of_monic_mem_map Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map
+-/
 
 end CommRing
 
@@ -173,6 +195,7 @@ section ScaleRoots
 
 variable {A : Type _} [CommRing R] [CommRing A]
 
+#print Polynomial.scaleRoots.isWeaklyEisensteinAt /-
 theorem scaleRoots.isWeaklyEisensteinAt (p : R[X]) {x : R} {P : Ideal R} (hP : x ∈ P) :
     (scaleRoots p x).IsWeaklyEisensteinAt P :=
   by
@@ -181,7 +204,14 @@ theorem scaleRoots.isWeaklyEisensteinAt (p : R[X]) {x : R} {P : Ideal R} (hP : x
   rw [nat_degree_scale_roots, ← tsub_pos_iff_lt] at hi
   exact Ideal.mul_mem_left _ _ (Ideal.pow_mem_of_mem P hP _ hi)
 #align polynomial.scale_roots.is_weakly_eisenstein_at Polynomial.scaleRoots.isWeaklyEisensteinAt
+-/
 
+/- warning: polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero -> Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Injective f) {p : R[X]}
     (hp : p.Monic) (x y : R) (z : A) (h : p.eval₂ f z = 0) (hz : f x * z = f y) :
     x ∣ y ^ p.natDegree :=
@@ -196,6 +226,12 @@ theorem dvd_pow_natDegree_of_eval₂_eq_zero {f : R →+* A} (hf : Function.Inje
   rwa [hz, Polynomial.eval₂_at_apply, hf] at this
 #align polynomial.dvd_pow_nat_degree_of_eval₂_eq_zero Polynomial.dvd_pow_natDegree_of_eval₂_eq_zero
 
+/- warning: polynomial.dvd_pow_nat_degree_of_aeval_eq_zero -> Polynomial.dvd_pow_natDegree_of_aeval_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_4 : Nontrivial.{u2} A] [_inst_5 : NoZeroSMulDivisors.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3)))))] {p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.Monic.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) A (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) A (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) A (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3) (Polynomial.aeval.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonUnitalNonAssocRing.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))))) -> (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (Ring.toDistrib.{u2} A (CommRing.toRing.{u2} A _inst_2)))) z (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) x)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))) (algebraMap.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) y)) -> (Dvd.Dvd.{u1} R (semigroupDvd.{u1} R (SemigroupWithZero.toSemigroup.{u1} R (NonUnitalSemiring.toSemigroupWithZero.{u1} R (NonUnitalRing.toNonUnitalSemiring.{u1} R (NonUnitalCommRing.toNonUnitalRing.{u1} R (CommRing.toNonUnitalCommRing.{u1} R _inst_1)))))) x (HPow.hPow.{u1, 0, u1} R Nat R (instHPow.{u1, 0} R Nat (Monoid.Pow.{u1} R (Ring.toMonoid.{u1} R (CommRing.toRing.{u1} R _inst_1)))) y (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) p))))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))] [_inst_4 : Nontrivial.{u1} A] [_inst_5 : NoZeroSMulDivisors.{u2, u1} R A (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommMonoidWithZero.toZero.{u1} A (CommSemiring.toCommMonoidWithZero.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))) (Algebra.toSMul.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3)] {p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))}, (Polynomial.Monic.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) p) -> (forall (x : R) (y : R) (z : A), (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))) (Algebra.toModule.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R 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(AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3 (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) A (CommRing.toCommSemiring.{u2} R _inst_1) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u2, u2} R R (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (Algebra.id.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) _inst_3))))) (Polynomial.aeval.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3 z) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) => A) p) _inst_2)))))) -> (Eq.{succ u1} A (HMul.hMul.{u1, u1, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) x) A (instHMul.{u1} A (NonUnitalNonAssocRing.toMul.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_2))))) z (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)))) R A (NonUnitalNonAssocSemiring.toMul.{u2} R 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_inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} R A (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2))))))) (algebraMap.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_2)) _inst_3) y)) -> (Dvd.dvd.{u2} R (semigroupDvd.{u2} R (SemigroupWithZero.toSemigroup.{u2} R (NonUnitalSemiring.toSemigroupWithZero.{u2} R (NonUnitalRing.toNonUnitalSemiring.{u2} R (NonUnitalCommRing.toNonUnitalRing.{u2} R (CommRing.toNonUnitalCommRing.{u2} R _inst_1)))))) x (HPow.hPow.{u2, 0, u2} R Nat R (instHPow.{u2, 0} R Nat (Monoid.Pow.{u2} R (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) y (Polynomial.natDegree.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) p))))
+Case conversion may be inaccurate. Consider using '#align polynomial.dvd_pow_nat_degree_of_aeval_eq_zero Polynomial.dvd_pow_natDegree_of_aeval_eq_zeroₓ'. -/
 theorem dvd_pow_natDegree_of_aeval_eq_zero [Algebra R A] [Nontrivial A] [NoZeroSMulDivisors R A]
     {p : R[X]} (hp : p.Monic) (x y : R) (z : A) (h : Polynomial.aeval z p = 0)
     (hz : z * algebraMap R A x = algebraMap R A y) : x ∣ y ^ p.natDegree :=
@@ -211,24 +247,40 @@ section CommSemiring
 
 variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsEisensteinAt 𝓟)
 
-theorem Polynomial.Monic.leadingCoeff_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤) : ¬f.leadingCoeff ∈ 𝓟 :=
+/- warning: polynomial.monic.leading_coeff_not_mem -> Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 𝓟 (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) -> (Not (Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) 𝓟))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 𝓟 (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) -> (Not (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.leadingCoeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) 𝓟))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.leading_coeff_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_memₓ'. -/
+theorem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤) :
+    ¬f.leadingCoeff ∈ 𝓟 :=
   hf.leadingCoeff.symm ▸ (Ideal.ne_top_iff_one _).1 h
-#align polynomial.monic.leading_coeff_not_mem Polynomial.Monic.leadingCoeff_not_mem
-
-theorem Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤)
-    (hmem : ∀ {n}, n < f.natDegree → f.coeff n ∈ 𝓟) (hnot_mem : f.coeff 0 ∉ 𝓟 ^ 2) :
+#align polynomial.monic.leading_coeff_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem
+
+/- warning: polynomial.monic.is_eisenstein_at_of_mem_of_not_mem -> Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 𝓟 (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.hasTop.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) -> (forall {n : Nat}, (LT.lt.{0} Nat Nat.hasLt n (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f)) -> (Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f n) 𝓟)) -> (Not (Membership.Mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.hasMem.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.idemSemiring.{u1, u1} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) 𝓟 (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))) -> (Polynomial.IsEisensteinAt.{u1} R _inst_1 f 𝓟)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {𝓟 : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)} {f : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Polynomial.Monic.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f) -> (Ne.{succ u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) 𝓟 (Top.top.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.instTopSubmodule.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) -> (forall {n : Nat}, (LT.lt.{0} Nat instLTNat n (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f)) -> (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f n) 𝓟)) -> (Not (Membership.mem.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (SetLike.instMembership.{u1, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) R (Submodule.setLike.{u1, u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1) f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HPow.hPow.{u1, 0, u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (instHPow.{u1, 0} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) Nat (Monoid.Pow.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toMonoidWithZero.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (IdemSemiring.toSemiring.{u1} (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.idemSemiring.{u1, u1} R _inst_1 R (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) 𝓟 (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) -> (Polynomial.IsEisensteinAt.{u1} R _inst_1 f 𝓟)
+Case conversion may be inaccurate. Consider using '#align polynomial.monic.is_eisenstein_at_of_mem_of_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_memₓ'. -/
+theorem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem (hf : f.Monic)
+    (h : 𝓟 ≠ ⊤) (hmem : ∀ {n}, n < f.natDegree → f.coeff n ∈ 𝓟) (hnot_mem : f.coeff 0 ∉ 𝓟 ^ 2) :
     f.IsEisensteinAt 𝓟 :=
   { leading := hf.leadingCoeff_not_mem h
     Mem := fun n hn => hmem hn
     not_mem := hnot_mem }
-#align polynomial.monic.is_eisenstein_at_of_mem_of_not_mem Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem
+#align polynomial.monic.is_eisenstein_at_of_mem_of_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem
 
 include hf
 
+#print Polynomial.IsEisensteinAt.isWeaklyEisensteinAt /-
 theorem isWeaklyEisensteinAt : IsWeaklyEisensteinAt f 𝓟 :=
   ⟨fun _ => hf.Mem⟩
 #align polynomial.is_eisenstein_at.is_weakly_eisenstein_at Polynomial.IsEisensteinAt.isWeaklyEisensteinAt
+-/
 
+#print Polynomial.IsEisensteinAt.coeff_mem /-
 theorem coeff_mem {n : ℕ} (hn : n ≠ f.natDegree) : f.coeff n ∈ 𝓟 :=
   by
   cases ne_iff_lt_or_gt.1 hn
@@ -236,6 +288,7 @@ theorem coeff_mem {n : ℕ} (hn : n ≠ f.natDegree) : f.coeff n ∈ 𝓟 :=
   · rw [coeff_eq_zero_of_nat_degree_lt h]
     exact Ideal.zero_mem _
 #align polynomial.is_eisenstein_at.coeff_mem Polynomial.IsEisensteinAt.coeff_mem
+-/
 
 end CommSemiring
 
@@ -243,6 +296,12 @@ section IsDomain
 
 variable [CommRing R] [IsDomain R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsEisensteinAt 𝓟)
 
+/- warning: polynomial.is_eisenstein_at.irreducible -> Polynomial.IsEisensteinAt.irreducible is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {𝓟 : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.IsEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 𝓟) -> (Polynomial.IsPrimitive.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f) -> (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f)) -> (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1))) f)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] {𝓟 : Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))} {f : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))}, (Polynomial.IsEisensteinAt.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f 𝓟) -> (Ideal.IsPrime.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 𝓟) -> (Polynomial.IsPrimitive.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1) f) -> (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) f)) -> (Irreducible.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MonoidWithZero.toMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toMonoidWithZero.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) f)
+Case conversion may be inaccurate. Consider using '#align polynomial.is_eisenstein_at.irreducible Polynomial.IsEisensteinAt.irreducibleₓ'. -/
 /-- If a primitive `f` satisfies `f.is_eisenstein_at 𝓟`, where `𝓟.is_prime`, then `f` is
 irreducible. -/
 theorem irreducible (hprime : 𝓟.IsPrime) (hu : f.IsPrimitive) (hfd0 : 0 < f.natDegree) :

2032a878

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

2032a878

chore: rename IsRoot.definition back to IsRoot.def (#11999)

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

1f25ef62

Diff

@@ -131,7 +131,7 @@ theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo
   obtain ⟨k, hk⟩ := exists_add_of_le hi
   rw [hk, pow_add]
   suffices x ^ f.natDegree ∈ 𝓟 by exact mul_mem_right (x ^ k) 𝓟 this
-  rw [IsRoot.definition, eval_eq_sum_range, Finset.range_add_one,
+  rw [IsRoot.def, eval_eq_sum_range, Finset.range_add_one,
     Finset.sum_insert Finset.not_mem_range_self, Finset.sum_range, hmo.coeff_natDegree, one_mul] at
     *
   rw [eq_neg_of_add_eq_zero_left hroot, Ideal.neg_mem_iff]
@@ -146,7 +146,7 @@ theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f
     obtain ⟨k, hk⟩ := exists_add_of_le hi
     rw [hk, pow_add]
     exact mul_mem_right _ _ this
-  rw [aeval_def, eval₂_eq_eval_map, ← IsRoot.definition] at hx
+  rw [aeval_def, eval₂_eq_eval_map, ← IsRoot.def] at hx
   exact pow_natDegree_le_of_root_of_monic_mem (hf.map _) hx (hmo.map _) _ rfl.le
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_aeval_zero_of_monic_mem_map Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map

2032a878

chore: rename away from 'def' (#11548)

This will become an error in 2024-03-16 nightly, possibly not permanently.

Co-authored-by: Scott Morrison <scott@tqft.net>

b505e8e9

Diff

@@ -131,7 +131,7 @@ theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo
   obtain ⟨k, hk⟩ := exists_add_of_le hi
   rw [hk, pow_add]
   suffices x ^ f.natDegree ∈ 𝓟 by exact mul_mem_right (x ^ k) 𝓟 this
-  rw [IsRoot.def, eval_eq_sum_range, Finset.range_add_one,
+  rw [IsRoot.definition, eval_eq_sum_range, Finset.range_add_one,
     Finset.sum_insert Finset.not_mem_range_self, Finset.sum_range, hmo.coeff_natDegree, one_mul] at
     *
   rw [eq_neg_of_add_eq_zero_left hroot, Ideal.neg_mem_iff]
@@ -146,7 +146,7 @@ theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f
     obtain ⟨k, hk⟩ := exists_add_of_le hi
     rw [hk, pow_add]
     exact mul_mem_right _ _ this
-  rw [aeval_def, eval₂_eq_eval_map, ← IsRoot.def] at hx
+  rw [aeval_def, eval₂_eq_eval_map, ← IsRoot.definition] at hx
   exact pow_natDegree_le_of_root_of_monic_mem (hf.map _) hx (hmo.map _) _ rfl.le
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_aeval_zero_of_monic_mem_map Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map

2032a878

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -74,7 +74,6 @@ end CommSemiring
 section CommRing
 
 variable [CommRing R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsWeaklyEisensteinAt 𝓟)
-
 variable {S : Type v} [CommRing S] [Algebra R S]
 
 section Principal

2032a878

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -90,7 +90,7 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo
   replace hx := eq_neg_of_add_eq_zero_left hx
   have : ∀ n < f.natDegree, p ∣ f.coeff n := by
     intro n hn
-    refine' mem_span_singleton.1 (by simpa using hf.mem hn)
+    exact mem_span_singleton.1 (by simpa using hf.mem hn)
   choose! φ hφ using this
   conv_rhs at hx =>
     congr
@@ -136,7 +136,7 @@ theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo
     Finset.sum_insert Finset.not_mem_range_self, Finset.sum_range, hmo.coeff_natDegree, one_mul] at
     *
   rw [eq_neg_of_add_eq_zero_left hroot, Ideal.neg_mem_iff]
-  refine' Submodule.sum_mem _ fun i _ => mul_mem_right _ _ (hf.mem (Fin.is_lt i))
+  exact Submodule.sum_mem _ fun i _ => mul_mem_right _ _ (hf.mem (Fin.is_lt i))
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem
 
 theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f = 0)
@@ -146,9 +146,9 @@ theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f
     intro i hi
     obtain ⟨k, hk⟩ := exists_add_of_le hi
     rw [hk, pow_add]
-    refine' mul_mem_right _ _ this
+    exact mul_mem_right _ _ this
   rw [aeval_def, eval₂_eq_eval_map, ← IsRoot.def] at hx
-  refine' pow_natDegree_le_of_root_of_monic_mem (hf.map _) hx (hmo.map _) _ rfl.le
+  exact pow_natDegree_le_of_root_of_monic_mem (hf.map _) hx (hmo.map _) _ rfl.le
 #align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_aeval_zero_of_monic_mem_map Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map
 
 end CommRing

2032a878

refactor: decapitalize names in @[mk_iff] (#9378)

@[mk_iff] class MyPred now generates myPred_iff, not MyPred_iff
add Lean.Name.decapitalize
fix indentation and a few typos in the docs/comments.

Partially addresses issue #9129

5192777c

Diff

@@ -64,7 +64,7 @@ variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsWeaklyEisenstein
 
 
 theorem map {A : Type v} [CommRing A] (φ : R →+* A) : (f.map φ).IsWeaklyEisensteinAt (𝓟.map φ) := by
-  refine' (IsWeaklyEisensteinAt_iff _ _).2 fun hn => _
+  refine' (isWeaklyEisensteinAt_iff _ _).2 fun hn => _
   rw [coeff_map]
   exact mem_map_of_mem _ (hf.mem (lt_of_lt_of_le hn (natDegree_map_le _ _)))
 #align polynomial.is_weakly_eisenstein_at.map Polynomial.IsWeaklyEisensteinAt.map

2032a878

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

@@ -157,7 +157,7 @@ end IsWeaklyEisensteinAt
 
 section ScaleRoots
 
-variable {A : Type _} [CommRing R] [CommRing A]
+variable {A : Type*} [CommRing R] [CommRing A]
 
 theorem scaleRoots.isWeaklyEisensteinAt (p : R[X]) {x : R} {P : Ideal R} (hP : x ∈ P) :
     (scaleRoots p x).IsWeaklyEisensteinAt P := by

2032a878

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) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.eisenstein.basic
-! leanprover-community/mathlib commit 2032a878972d5672e7c27c957e7a6e297b044973
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.EisensteinCriterion
 import Mathlib.RingTheory.Polynomial.ScaleRoots
 
+#align_import ring_theory.polynomial.eisenstein.basic from "leanprover-community/mathlib"@"2032a878972d5672e7c27c957e7a6e297b044973"
+
 /-!
 # Eisenstein polynomials
 Given an ideal `𝓟` of a commutative semiring `R`, we say that a polynomial `f : R[X]` is

2032a878

feat: port RingTheory.Polynomial.Eisenstein.IsIntegral (#5302)

Fix also some names in RingTheory.Polynomial.Eisenstein.Basic that are in the wrong namespace.

c511043c

Diff

@@ -198,17 +198,17 @@ section CommSemiring
 
 variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsEisensteinAt 𝓟)
 
-theorem Polynomial.Monic.leadingCoeff_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤) : ¬f.leadingCoeff ∈ 𝓟 :=
-  hf.leadingCoeff.symm ▸ (Ideal.ne_top_iff_one _).1 h
-#align polynomial.monic.leading_coeff_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem
+theorem _root_.Polynomial.Monic.leadingCoeff_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤) :
+    ¬f.leadingCoeff ∈ 𝓟 := hf.leadingCoeff.symm ▸ (Ideal.ne_top_iff_one _).1 h
+#align polynomial.monic.leading_coeff_not_mem Polynomial.Monic.leadingCoeff_not_mem
 
-theorem Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤)
+theorem _root_.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤)
     (hmem : ∀ {n}, n < f.natDegree → f.coeff n ∈ 𝓟) (hnot_mem : f.coeff 0 ∉ 𝓟 ^ 2) :
     f.IsEisensteinAt 𝓟 :=
-  { leading := leadingCoeff_not_mem hf h
+  { leading := Polynomial.Monic.leadingCoeff_not_mem hf h
     mem := fun hn => hmem hn
     not_mem := hnot_mem }
-#align polynomial.monic.is_eisenstein_at_of_mem_of_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem
+#align polynomial.monic.is_eisenstein_at_of_mem_of_not_mem Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem
 
 theorem isWeaklyEisensteinAt : IsWeaklyEisensteinAt f 𝓟 :=
   ⟨fun h => hf.mem h⟩

2032a878

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
removes many but not quite all set_option maxHeartbeats commands
makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

a6e1045f

Diff

@@ -65,7 +65,6 @@ section CommSemiring
 
 variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsWeaklyEisensteinAt 𝓟)
 
-set_option synthInstance.etaExperiment true
 
 theorem map {A : Type v} [CommRing A] (φ : R →+* A) : (f.map φ).IsWeaklyEisensteinAt (𝓟.map φ) := by
   refine' (IsWeaklyEisensteinAt_iff _ _).2 fun hn => _

2032a878

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

@@ -67,8 +67,7 @@ variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsWeaklyEisenstein
 
 set_option synthInstance.etaExperiment true
 
-theorem map {A : Type v} [CommRing A] (φ : R →+* A) : (f.map φ).IsWeaklyEisensteinAt (𝓟.map φ) :=
-  by
+theorem map {A : Type v} [CommRing A] (φ : R →+* A) : (f.map φ).IsWeaklyEisensteinAt (𝓟.map φ) := by
   refine' (IsWeaklyEisensteinAt_iff _ _).2 fun hn => _
   rw [coeff_map]
   exact mem_map_of_mem _ (hf.mem (lt_of_lt_of_le hn (natDegree_map_le _ _)))
@@ -87,9 +86,8 @@ section Principal
 variable {p : R}
 
 theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo : f.Monic)
-    (hf : f.IsWeaklyEisensteinAt (Submodule.span R {p})) :
-    ∃ y ∈ adjoin R ({x} : Set S), (algebraMap R S) p * y = x ^ (f.map (algebraMap R S)).natDegree :=
-  by
+    (hf : f.IsWeaklyEisensteinAt (Submodule.span R {p})) : ∃ y ∈ adjoin R ({x} : Set S),
+    (algebraMap R S) p * y = x ^ (f.map (algebraMap R S)).natDegree := by
   rw [aeval_def, Polynomial.eval₂_eq_eval_map, eval_eq_sum_range, range_add_one,
     sum_insert not_mem_range_self, sum_range, (hmo.map (algebraMap R S)).coeff_natDegree,
     one_mul] at hx

2032a878

chore: fix #align lines (#3640)

This PR fixes two things:

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

2b42dc7c

Diff

@@ -113,8 +113,7 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree {x : S} (hx : aeval x f = 0) (hmo
       (Subalgebra.sum_mem _ fun i _ =>
         Subalgebra.mul_mem _ (Subalgebra.algebraMap_mem _ _)
           (Subalgebra.pow_mem _ (subset_adjoin (Set.mem_singleton x)) _))
-#align polynomial.is_weakly_eisenstein_at.exists_mem_adjoin_mul_eq_pow_nat_degree
-Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree
+#align polynomial.is_weakly_eisenstein_at.exists_mem_adjoin_mul_eq_pow_nat_degree Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree
 
 theorem exists_mem_adjoin_mul_eq_pow_natDegree_le {x : S} (hx : aeval x f = 0) (hmo : f.Monic)
     (hf : f.IsWeaklyEisensteinAt (Submodule.span R {p})) :
@@ -127,8 +126,7 @@ theorem exists_mem_adjoin_mul_eq_pow_natDegree_le {x : S} (hx : aeval x f = 0) (
   refine' ⟨y * x ^ k, _, _⟩
   · exact Subalgebra.mul_mem _ hy (Subalgebra.pow_mem _ (subset_adjoin (Set.mem_singleton x)) _)
   · rw [← mul_assoc _ y, H]
-#align polynomial.is_weakly_eisenstein_at.exists_mem_adjoin_mul_eq_pow_nat_degree_le
-Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le
+#align polynomial.is_weakly_eisenstein_at.exists_mem_adjoin_mul_eq_pow_nat_degree_le Polynomial.IsWeaklyEisensteinAt.exists_mem_adjoin_mul_eq_pow_natDegree_le
 
 end Principal
 
@@ -145,8 +143,7 @@ theorem pow_natDegree_le_of_root_of_monic_mem {x : R} (hroot : IsRoot f x) (hmo
     *
   rw [eq_neg_of_add_eq_zero_left hroot, Ideal.neg_mem_iff]
   refine' Submodule.sum_mem _ fun i _ => mul_mem_right _ _ (hf.mem (Fin.is_lt i))
-#align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem
-Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem
+#align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_root_of_monic_mem Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_root_of_monic_mem
 
 theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f = 0)
     (hmo : f.Monic) :
@@ -158,8 +155,7 @@ theorem pow_natDegree_le_of_aeval_zero_of_monic_mem_map {x : S} (hx : aeval x f
     refine' mul_mem_right _ _ this
   rw [aeval_def, eval₂_eq_eval_map, ← IsRoot.def] at hx
   refine' pow_natDegree_le_of_root_of_monic_mem (hf.map _) hx (hmo.map _) _ rfl.le
-#align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_aeval_zero_of_monic_mem_map
-Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map
+#align polynomial.is_weakly_eisenstein_at.pow_nat_degree_le_of_aeval_zero_of_monic_mem_map Polynomial.IsWeaklyEisensteinAt.pow_natDegree_le_of_aeval_zero_of_monic_mem_map
 
 end CommRing
 
@@ -207,8 +203,7 @@ variable [CommSemiring R] {𝓟 : Ideal R} {f : R[X]} (hf : f.IsEisensteinAt 
 
 theorem Polynomial.Monic.leadingCoeff_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤) : ¬f.leadingCoeff ∈ 𝓟 :=
   hf.leadingCoeff.symm ▸ (Ideal.ne_top_iff_one _).1 h
-#align polynomial.monic.leading_coeff_not_mem
-Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem
+#align polynomial.monic.leading_coeff_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.leadingCoeff_not_mem
 
 theorem Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem (hf : f.Monic) (h : 𝓟 ≠ ⊤)
     (hmem : ∀ {n}, n < f.natDegree → f.coeff n ∈ 𝓟) (hnot_mem : f.coeff 0 ∉ 𝓟 ^ 2) :
@@ -216,13 +211,11 @@ theorem Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem (hf : f.Monic) (h : 
   { leading := leadingCoeff_not_mem hf h
     mem := fun hn => hmem hn
     not_mem := hnot_mem }
-#align polynomial.monic.is_eisenstein_at_of_mem_of_not_mem
-Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem
+#align polynomial.monic.is_eisenstein_at_of_mem_of_not_mem Polynomial.IsEisensteinAt.Polynomial.Monic.isEisensteinAt_of_mem_of_not_mem
 
 theorem isWeaklyEisensteinAt : IsWeaklyEisensteinAt f 𝓟 :=
   ⟨fun h => hf.mem h⟩
-#align polynomial.is_eisenstein_at.is_weakly_eisenstein_at
-Polynomial.IsEisensteinAt.isWeaklyEisensteinAt
+#align polynomial.is_eisenstein_at.is_weakly_eisenstein_at Polynomial.IsEisensteinAt.isWeaklyEisensteinAt
 
 theorem coeff_mem {n : ℕ} (hn : n ≠ f.natDegree) : f.coeff n ∈ 𝓟 := by
   cases' ne_iff_lt_or_gt.1 hn with h₁ h₂

2032a878

feat: port RingTheory.Polynomial.Eisenstein.Basic (#3382)

5771d641

`ring_theory.polynomial.eisenstein.basic` ⟷ `Mathlib.RingTheory.Polynomial.Eisenstein.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 515

ring_theory.polynomial.eisenstein.basic ⟷ Mathlib.RingTheory.Polynomial.Eisenstein.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 515

`ring_theory.polynomial.eisenstein.basic` ⟷ `Mathlib.RingTheory.Polynomial.Eisenstein.Basic`