ring_theory.polynomial.scale_roots | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

40ac1b25

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

10bf4f82

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Devon Tuma
 -/
 import Algebra.GroupWithZero.NonZeroDivisors
-import Data.Polynomial.AlgebraMap
+import Algebra.Polynomial.AlgebraMap
 
 #align_import ring_theory.polynomial.scale_roots from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"

10bf4f82

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Devon Tuma
 -/
-import RingTheory.NonZeroDivisors
+import Algebra.GroupWithZero.NonZeroDivisors
 import Data.Polynomial.AlgebraMap
 
 #align_import ring_theory.polynomial.scale_roots from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
@@ -160,7 +160,7 @@ theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+
     (hs : s ∈ nonZeroDivisors A) : eval₂ f (f r) (scaleRoots p s) = 0 :=
   by
   convert scale_roots_eval₂_eq_zero f hr
-  rw [← mul_div_assoc, mul_comm, mul_div_cancel]
+  rw [← mul_div_assoc, mul_comm, mul_div_cancel_right₀]
   exact map_ne_zero_of_mem_nonZeroDivisors _ hf hs
 #align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero
 -/

10bf4f82

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -62,7 +62,7 @@ theorem scaleRoots_ne_zero {p : R[X]} (hp : p ≠ 0) (s : R) : scaleRoots p s 
   have : p.coeff p.nat_degree ≠ 0 := mt leading_coeff_eq_zero.mp hp
   have : (scale_roots p s).coeff p.nat_degree = 0 :=
     congr_fun (congr_arg (coeff : R[X] → ℕ → R) h) p.nat_degree
-  rw [coeff_scale_roots_nat_degree] at this 
+  rw [coeff_scale_roots_nat_degree] at this
   contradiction
 #align polynomial.scale_roots_ne_zero Polynomial.scaleRoots_ne_zero
 -/

10bf4f82

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Devon Tuma
 -/
-import Mathbin.RingTheory.NonZeroDivisors
-import Mathbin.Data.Polynomial.AlgebraMap
+import RingTheory.NonZeroDivisors
+import Data.Polynomial.AlgebraMap
 
 #align_import ring_theory.polynomial.scale_roots from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"

10bf4f82

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Devon Tuma
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.scale_roots
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.NonZeroDivisors
 import Mathbin.Data.Polynomial.AlgebraMap
 
+#align_import ring_theory.polynomial.scale_roots from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
 /-!
 # Scaling the roots of a polynomial

10bf4f82

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -37,11 +37,13 @@ noncomputable def scaleRoots (p : R[X]) (s : R) : R[X] :=
 #align polynomial.scale_roots Polynomial.scaleRoots
 -/
 
+#print Polynomial.coeff_scaleRoots /-
 @[simp]
 theorem coeff_scaleRoots (p : R[X]) (s : R) (i : ℕ) :
     (scaleRoots p s).coeff i = coeff p i * s ^ (p.natDegree - i) := by
   simp (config := { contextual := true }) [scale_roots, coeff_monomial]
 #align polynomial.coeff_scale_roots Polynomial.coeff_scaleRoots
+-/
 
 #print Polynomial.coeff_scaleRoots_natDegree /-
 theorem coeff_scaleRoots_natDegree (p : R[X]) (s : R) :
@@ -74,6 +76,7 @@ theorem support_scaleRoots_le (p : R[X]) (s : R) : (scaleRoots p s).support ≤
 #align polynomial.support_scale_roots_le Polynomial.support_scaleRoots_le
 -/
 
+#print Polynomial.support_scaleRoots_eq /-
 theorem support_scaleRoots_eq (p : R[X]) {s : R} (hs : s ∈ nonZeroDivisors R) :
     (scaleRoots p s).support = p.support :=
   le_antisymm (support_scaleRoots_le p s)
@@ -84,6 +87,7 @@ theorem support_scaleRoots_eq (p : R[X]) {s : R} (hs : s ∈ nonZeroDivisors R)
       have := pow_mem hs (p.nat_degree - i) _ ps_zero
       contradiction)
 #align polynomial.support_scale_roots_eq Polynomial.support_scaleRoots_eq
+-/
 
 #print Polynomial.degree_scaleRoots /-
 @[simp]
@@ -114,6 +118,7 @@ theorem monic_scaleRoots_iff {p : R[X]} (s : R) : Monic (scaleRoots p s) ↔ Mon
 #align polynomial.monic_scale_roots_iff Polynomial.monic_scaleRoots_iff
 -/
 
+#print Polynomial.scaleRoots_eval₂_mul /-
 theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     eval₂ f (f s * r) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f r p :=
   calc
@@ -137,16 +142,22 @@ theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     _ = f s ^ p.natDegree * p.support.Sum fun i : ℕ => f (p.coeff i) * r ^ i := Finset.mul_sum.symm
     _ = f s ^ p.natDegree * eval₂ f r p := by simp [eval₂_eq_sum, sum_def]
 #align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mul
+-/
 
+#print Polynomial.scaleRoots_eval₂_eq_zero /-
 theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (hr : eval₂ f r p = 0) :
     eval₂ f (f s * r) (scaleRoots p s) = 0 := by rw [scale_roots_eval₂_mul, hr, _root_.mul_zero]
 #align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zero
+-/
 
+#print Polynomial.scaleRoots_aeval_eq_zero /-
 theorem scaleRoots_aeval_eq_zero [Algebra S R] {p : S[X]} {r : R} {s : S} (hr : aeval r p = 0) :
     aeval (algebraMap S R s * r) (scaleRoots p s) = 0 :=
   scaleRoots_eval₂_eq_zero (algebraMap S R) hr
 #align polynomial.scale_roots_aeval_eq_zero Polynomial.scaleRoots_aeval_eq_zero
+-/
 
+#print Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero /-
 theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+* K}
     (hf : Function.Injective f) {r s : A} (hr : eval₂ f (f r / f s) p = 0)
     (hs : s ∈ nonZeroDivisors A) : eval₂ f (f r) (scaleRoots p s) = 0 :=
@@ -155,20 +166,25 @@ theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+
   rw [← mul_div_assoc, mul_comm, mul_div_cancel]
   exact map_ne_zero_of_mem_nonZeroDivisors _ hf hs
 #align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero
+-/
 
+#print Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero /-
 theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
     (inj : Function.Injective (algebraMap A K)) {p : A[X]} {r s : A}
     (hr : aeval (algebraMap A K r / algebraMap A K s) p = 0) (hs : s ∈ nonZeroDivisors A) :
     aeval (algebraMap A K r) (scaleRoots p s) = 0 :=
   scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero inj hr hs
 #align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero
+-/
 
+#print Polynomial.map_scaleRoots /-
 theorem map_scaleRoots (p : R[X]) (x : R) (f : R →+* S) (h : f p.leadingCoeff ≠ 0) :
     (p.scaleRoots x).map f = (p.map f).scaleRoots (f x) :=
   by
   ext
   simp [Polynomial.natDegree_map_of_leadingCoeff_ne_zero _ h]
 #align polynomial.map_scale_roots Polynomial.map_scaleRoots
+-/
 
 end Polynomial

10bf4f82

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -136,7 +136,6 @@ theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
         exact le_nat_degree_of_ne_zero (polynomial.mem_support_iff.mp hi))
     _ = f s ^ p.natDegree * p.support.Sum fun i : ℕ => f (p.coeff i) * r ^ i := Finset.mul_sum.symm
     _ = f s ^ p.natDegree * eval₂ f r p := by simp [eval₂_eq_sum, sum_def]
-    
 #align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mul
 
 theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (hr : eval₂ f r p = 0) :

10bf4f82

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -63,14 +63,14 @@ theorem scaleRoots_ne_zero {p : R[X]} (hp : p ≠ 0) (s : R) : scaleRoots p s 
   have : p.coeff p.nat_degree ≠ 0 := mt leading_coeff_eq_zero.mp hp
   have : (scale_roots p s).coeff p.nat_degree = 0 :=
     congr_fun (congr_arg (coeff : R[X] → ℕ → R) h) p.nat_degree
-  rw [coeff_scale_roots_nat_degree] at this
+  rw [coeff_scale_roots_nat_degree] at this 
   contradiction
 #align polynomial.scale_roots_ne_zero Polynomial.scaleRoots_ne_zero
 -/
 
 #print Polynomial.support_scaleRoots_le /-
-theorem support_scaleRoots_le (p : R[X]) (s : R) : (scaleRoots p s).support ≤ p.support := by
-  intro ; simpa using left_ne_zero_of_mul
+theorem support_scaleRoots_le (p : R[X]) (s : R) : (scaleRoots p s).support ≤ p.support := by intro;
+  simpa using left_ne_zero_of_mul
 #align polynomial.support_scale_roots_le Polynomial.support_scaleRoots_le
 -/

10bf4f82

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -143,12 +143,10 @@ theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (h
     eval₂ f (f s * r) (scaleRoots p s) = 0 := by rw [scale_roots_eval₂_mul, hr, _root_.mul_zero]
 #align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zero
 
-#print Polynomial.scaleRoots_aeval_eq_zero /-
 theorem scaleRoots_aeval_eq_zero [Algebra S R] {p : S[X]} {r : R} {s : S} (hr : aeval r p = 0) :
     aeval (algebraMap S R s * r) (scaleRoots p s) = 0 :=
   scaleRoots_eval₂_eq_zero (algebraMap S R) hr
 #align polynomial.scale_roots_aeval_eq_zero Polynomial.scaleRoots_aeval_eq_zero
--/
 
 theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+* K}
     (hf : Function.Injective f) {r s : A} (hr : eval₂ f (f r / f s) p = 0)

10bf4f82

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -28,7 +28,7 @@ variable {M : Submonoid A}
 
 namespace Polynomial
 
-open BigOperators Polynomial
+open scoped BigOperators Polynomial
 
 #print Polynomial.scaleRoots /-
 /-- `scale_roots p s` is a polynomial with root `r * s` for each root `r` of `p`. -/
@@ -68,9 +68,11 @@ theorem scaleRoots_ne_zero {p : R[X]} (hp : p ≠ 0) (s : R) : scaleRoots p s 
 #align polynomial.scale_roots_ne_zero Polynomial.scaleRoots_ne_zero
 -/
 
+#print Polynomial.support_scaleRoots_le /-
 theorem support_scaleRoots_le (p : R[X]) (s : R) : (scaleRoots p s).support ≤ p.support := by
   intro ; simpa using left_ne_zero_of_mul
 #align polynomial.support_scale_roots_le Polynomial.support_scaleRoots_le
+-/
 
 theorem support_scaleRoots_eq (p : R[X]) {s : R} (hs : s ∈ nonZeroDivisors R) :
     (scaleRoots p s).support = p.support :=

10bf4f82

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -37,12 +37,6 @@ noncomputable def scaleRoots (p : R[X]) (s : R) : R[X] :=
 #align polynomial.scale_roots Polynomial.scaleRoots
 -/
 
-/- warning: polynomial.coeff_scale_roots -> Polynomial.coeff_scaleRoots is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) (s : R) (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s) i) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p i) (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_4)))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p) i)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (s : R) (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s) i) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) p i) (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_4)))))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) p) i)))
-Case conversion may be inaccurate. Consider using '#align polynomial.coeff_scale_roots Polynomial.coeff_scaleRootsₓ'. -/
 @[simp]
 theorem coeff_scaleRoots (p : R[X]) (s : R) (i : ℕ) :
     (scaleRoots p s).coeff i = coeff p i * s ^ (p.natDegree - i) := by
@@ -74,22 +68,10 @@ theorem scaleRoots_ne_zero {p : R[X]} (hp : p ≠ 0) (s : R) : scaleRoots p s 
 #align polynomial.scale_roots_ne_zero Polynomial.scaleRoots_ne_zero
 -/
 
-/- warning: polynomial.support_scale_roots_le -> Polynomial.support_scaleRoots_le is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) (s : R), LE.le.{0} (Finset.{0} Nat) (Preorder.toHasLe.{0} (Finset.{0} Nat) (PartialOrder.toPreorder.{0} (Finset.{0} Nat) (Finset.partialOrder.{0} Nat))) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s)) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (s : R), LE.le.{0} (Finset.{0} Nat) (Preorder.toLE.{0} (Finset.{0} Nat) (PartialOrder.toPreorder.{0} (Finset.{0} Nat) (Finset.partialOrder.{0} Nat))) (Polynomial.support.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s)) (Polynomial.support.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) p)
-Case conversion may be inaccurate. Consider using '#align polynomial.support_scale_roots_le Polynomial.support_scaleRoots_leₓ'. -/
 theorem support_scaleRoots_le (p : R[X]) (s : R) : (scaleRoots p s).support ≤ p.support := by
   intro ; simpa using left_ne_zero_of_mul
 #align polynomial.support_scale_roots_le Polynomial.support_scaleRoots_le
 
-/- warning: polynomial.support_scale_roots_eq -> Polynomial.support_scaleRoots_eq is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) {s : R}, (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))))))) s (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))))) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s)) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align polynomial.support_scale_roots_eq Polynomial.support_scaleRoots_eqₓ'. -/
 theorem support_scaleRoots_eq (p : R[X]) {s : R} (hs : s ∈ nonZeroDivisors R) :
     (scaleRoots p s).support = p.support :=
   le_antisymm (support_scaleRoots_le p s)
@@ -130,9 +112,6 @@ theorem monic_scaleRoots_iff {p : R[X]} (s : R) : Monic (scaleRoots p s) ↔ Mon
 #align polynomial.monic_scale_roots_iff Polynomial.monic_scaleRoots_iff
 -/
 
-/- warning: polynomial.scale_roots_eval₂_mul -> Polynomial.scaleRoots_eval₂_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mulₓ'. -/
 theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     eval₂ f (f s * r) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f r p :=
   calc
@@ -158,9 +137,6 @@ theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     
 #align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mul
 
-/- warning: polynomial.scale_roots_eval₂_eq_zero -> Polynomial.scaleRoots_eval₂_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zeroₓ'. -/
 theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (hr : eval₂ f r p = 0) :
     eval₂ f (f s * r) (scaleRoots p s) = 0 := by rw [scale_roots_eval₂_mul, hr, _root_.mul_zero]
 #align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zero
@@ -172,9 +148,6 @@ theorem scaleRoots_aeval_eq_zero [Algebra S R] {p : S[X]} {r : R} {s : S} (hr :
 #align polynomial.scale_roots_aeval_eq_zero Polynomial.scaleRoots_aeval_eq_zero
 -/
 
-/- warning: polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero -> Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zeroₓ'. -/
 theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+* K}
     (hf : Function.Injective f) {r s : A} (hr : eval₂ f (f r / f s) p = 0)
     (hs : s ∈ nonZeroDivisors A) : eval₂ f (f r) (scaleRoots p s) = 0 :=
@@ -184,9 +157,6 @@ theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+
   exact map_ne_zero_of_mem_nonZeroDivisors _ hf hs
 #align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero
 
-/- warning: polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero -> Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zeroₓ'. -/
 theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
     (inj : Function.Injective (algebraMap A K)) {p : A[X]} {r s : A}
     (hr : aeval (algebraMap A K r / algebraMap A K s) p = 0) (hs : s ∈ nonZeroDivisors A) :
@@ -194,9 +164,6 @@ theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
   scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero inj hr hs
 #align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero
 
-/- warning: polynomial.map_scale_roots -> Polynomial.map_scaleRoots is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.map_scale_roots Polynomial.map_scaleRootsₓ'. -/
 theorem map_scaleRoots (p : R[X]) (x : R) (f : R →+* S) (h : f p.leadingCoeff ≠ 0) :
     (p.scaleRoots x).map f = (p.map f).scaleRoots (f x) :=
   by

10bf4f82

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -58,10 +58,7 @@ theorem coeff_scaleRoots_natDegree (p : R[X]) (s : R) :
 
 #print Polynomial.zero_scaleRoots /-
 @[simp]
-theorem zero_scaleRoots (s : R) : scaleRoots 0 s = 0 :=
-  by
-  ext
-  simp
+theorem zero_scaleRoots (s : R) : scaleRoots 0 s = 0 := by ext; simp
 #align polynomial.zero_scale_roots Polynomial.zero_scaleRoots
 -/
 
@@ -83,10 +80,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (s : R), LE.le.{0} (Finset.{0} Nat) (Preorder.toLE.{0} (Finset.{0} Nat) (PartialOrder.toPreorder.{0} (Finset.{0} Nat) (Finset.partialOrder.{0} Nat))) (Polynomial.support.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s)) (Polynomial.support.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.support_scale_roots_le Polynomial.support_scaleRoots_leₓ'. -/
-theorem support_scaleRoots_le (p : R[X]) (s : R) : (scaleRoots p s).support ≤ p.support :=
-  by
-  intro
-  simpa using left_ne_zero_of_mul
+theorem support_scaleRoots_le (p : R[X]) (s : R) : (scaleRoots p s).support ≤ p.support := by
+  intro ; simpa using left_ne_zero_of_mul
 #align polynomial.support_scale_roots_le Polynomial.support_scaleRoots_le
 
 /- warning: polynomial.support_scale_roots_eq -> Polynomial.support_scaleRoots_eq is a dubious translation:

10bf4f82

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -136,10 +136,7 @@ theorem monic_scaleRoots_iff {p : R[X]} (s : R) : Monic (scaleRoots p s) ↔ Mon
 -/
 
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 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mulₓ'. -/
 theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     eval₂ f (f s * r) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f r p :=
@@ -167,10 +164,7 @@ theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
 #align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mul
 
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 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zeroₓ'. -/
 theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (hr : eval₂ f r p = 0) :
     eval₂ f (f s * r) (scaleRoots p s) = 0 := by rw [scale_roots_eval₂_mul, hr, _root_.mul_zero]
@@ -184,10 +178,7 @@ theorem scaleRoots_aeval_eq_zero [Algebra S R] {p : S[X]} {r : R} {s : S} (hr :
 -/
 
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(Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_3))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zeroₓ'. -/
 theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+* K}
     (hf : Function.Injective f) {r s : A} (hr : eval₂ f (f r / f s) p = 0)
@@ -199,10 +190,7 @@ theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+
 #align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero
 
 /- warning: polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero -> Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero is a dubious translation:
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(CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (fun (_x : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) 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(Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) s))) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) p) 0 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(Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) p) _inst_3))))))) -> (Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) s (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (fun (_x : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6))))) (Polynomial.aeval.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) r)) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) _inst_3))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zeroₓ'. -/
 theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
     (inj : Function.Injective (algebraMap A K)) {p : A[X]} {r s : A}
@@ -212,10 +200,7 @@ theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
 #align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero
 
 /- warning: polynomial.map_scale_roots -> Polynomial.map_scaleRoots is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.map_scale_roots Polynomial.map_scaleRootsₓ'. -/
 theorem map_scaleRoots (p : R[X]) (x : R) (f : R →+* S) (h : f p.leadingCoeff ≠ 0) :
     (p.scaleRoots x).map f = (p.map f).scaleRoots (f x) :=

10bf4f82

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -202,7 +202,7 @@ theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+
 lean 3 declaration is
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 but is expected to have type
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(CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A 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A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6))))) (Polynomial.aeval.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) r)) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) _inst_3))))))))
+  forall {A : Type.{u2}} {K : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_3 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))], (Function.Injective.{succ u2, succ u1} A K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6))) -> (forall {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {r : A} {s : A}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A 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(x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} 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(CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6))))) (Polynomial.aeval.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) r)) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zeroₓ'. -/
 theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
     (inj : Function.Injective (algebraMap A K)) {p : A[X]} {r s : A}

10bf4f82

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -139,7 +139,7 @@ theorem monic_scaleRoots_iff {p : R[X]} (s : R) : Monic (scaleRoots p s) ↔ Mon
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (r : R) (s : S), Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (fun (_x : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) => S -> R) (RingHom.hasCoeToFun.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (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_4)))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (fun (_x : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) => S -> R) (RingHom.hasCoeToFun.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) f s) (Polynomial.natDegree.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) p)) (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f r p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (r : R) (s : S), Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4))))) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))) f s) (Polynomial.natDegree.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) p)) (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f r p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (r : R) (s : S), Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) _inst_4))))) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) _inst_4)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))) f s) (Polynomial.natDegree.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) p)) (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f r p))
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mulₓ'. -/
 theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     eval₂ f (f s * r) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f r p :=
@@ -170,7 +170,7 @@ theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) {r : R} {s : S}, (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f r p) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (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_4)))))))))) -> (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (fun (_x : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) => S -> R) (RingHom.hasCoeToFun.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (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_4))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) {r : R} {s : S}, (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f r p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))))) -> (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) {r : R} {s : S}, (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f r p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))))) -> (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) s) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zeroₓ'. -/
 theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (hr : eval₂ f r p = 0) :
     eval₂ f (f s * r) (scaleRoots p s) = 0 := by rw [scale_roots_eval₂_mul, hr, _root_.mul_zero]
@@ -187,7 +187,7 @@ theorem scaleRoots_aeval_eq_zero [Algebra S R] {p : S[X]} {r : R} {s : S} (hr :
 lean 3 declaration is
   forall {A : Type.{u1}} {K : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_3 : Field.{u2} K] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))}, (Function.Injective.{succ u1, succ u2} A K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) f)) -> (forall {r : A} {s : A}, (Eq.{succ u2} K (Polynomial.eval₂.{u1, u2} A K (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) f (HDiv.hDiv.{u2, u2, u2} K K K (instHDiv.{u2} K (DivInvMonoid.toHasDiv.{u2} K (DivisionRing.toDivInvMonoid.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) f r) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) f s)) p) (OfNat.ofNat.{u2} K 0 (OfNat.mk.{u2} K 0 (Zero.zero.{u2} K (MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))))))))) -> (Membership.Mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))))) s (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))) -> (Eq.{succ u2} K (Polynomial.eval₂.{u1, u2} A K (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) f (coeFn.{max (succ u1) (succ u2), 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(NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))))))))))
 but is expected to have type
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(CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f)) -> (forall {r : A} {s : A}, (Eq.{succ u1} K (Polynomial.eval₂.{u2, u1} A K (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) f (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) s) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (instHDiv.{u1} ((fun 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(Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f r) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f s)) p) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K 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(Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_3))))))))
+  forall {A : Type.{u2}} {K : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_3 : Field.{u1} K] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))}, (Function.Injective.{succ u2, succ u1} A K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f)) -> (forall {r : A} {s : A}, (Eq.{succ u1} K (Polynomial.eval₂.{u2, u1} A K (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) f (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) s) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (instHDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f s)) p) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_3))))))) -> (Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) s (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) -> (Eq.{succ u1} K (Polynomial.eval₂.{u2, u1} A K (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) f (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zeroₓ'. -/
 theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+* K}
     (hf : Function.Injective f) {r s : A} (hr : eval₂ f (f r / f s) p = 0)
@@ -202,7 +202,7 @@ theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+
 lean 3 declaration is
   forall {A : Type.{u1}} {K : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_3 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))], (Function.Injective.{succ u1, succ u2} A K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) _inst_6))) -> (forall {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {r : A} {s : A}, (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) K (CommRing.toCommSemiring.{u1} A _inst_1) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) 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(Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) _inst_6) r)) (Polynomial.scaleRoots.{u1} A _inst_1 p s)) (OfNat.ofNat.{u2} K 0 (OfNat.mk.{u2} K 0 (Zero.zero.{u2} K (MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))))))))))
 but is expected to have type
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(x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) 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(Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun 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(Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6))))) (Polynomial.aeval.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) r)) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) _inst_3))))))))
+  forall {A : Type.{u2}} {K : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_3 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))], (Function.Injective.{succ u2, succ u1} A K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6))) -> (forall {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {r : A} {s : A}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (fun (_x : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun 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(Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => 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A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) s))) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) p) 0 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(Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) p) _inst_3))))))) -> (Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) s (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (fun (_x : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6))))) (Polynomial.aeval.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) _inst_3))) _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) r)) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zeroₓ'. -/
 theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
     (inj : Function.Injective (algebraMap A K)) {p : A[X]} {r s : A}
@@ -215,7 +215,7 @@ theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) (x : R) (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) f (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))))))))) -> (Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) f (Polynomial.scaleRoots.{u1} R _inst_4 p x)) (Polynomial.scaleRoots.{u2} S _inst_5 (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) f p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) f x)))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : CommRing.{u2} R] [_inst_5 : CommRing.{u1} S] (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (x : R) (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))), (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) f (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) _inst_5)))))) -> (Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (Polynomial.map.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) f (Polynomial.scaleRoots.{u2} R _inst_4 p x)) (Polynomial.scaleRoots.{u1} S _inst_5 (Polynomial.map.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) f x)))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : CommRing.{u2} R] [_inst_5 : CommRing.{u1} S] (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (x : R) (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))), (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) f (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) _inst_5)))))) -> (Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (Polynomial.map.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) f (Polynomial.scaleRoots.{u2} R _inst_4 p x)) (Polynomial.scaleRoots.{u1} S _inst_5 (Polynomial.map.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) f x)))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_scale_roots Polynomial.map_scaleRootsₓ'. -/
 theorem map_scaleRoots (p : R[X]) (x : R) (f : R →+* S) (h : f p.leadingCoeff ≠ 0) :
     (p.scaleRoots x).map f = (p.map f).scaleRoots (f x) :=

10bf4f82

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -77,13 +77,17 @@ theorem scaleRoots_ne_zero {p : R[X]} (hp : p ≠ 0) (s : R) : scaleRoots p s 
 #align polynomial.scale_roots_ne_zero Polynomial.scaleRoots_ne_zero
 -/
 
-#print Polynomial.support_scaleRoots_le /-
+/- warning: polynomial.support_scale_roots_le -> Polynomial.support_scaleRoots_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) (s : R), LE.le.{0} (Finset.{0} Nat) (Preorder.toHasLe.{0} (Finset.{0} Nat) (PartialOrder.toPreorder.{0} (Finset.{0} Nat) (Finset.partialOrder.{0} Nat))) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s)) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (s : R), LE.le.{0} (Finset.{0} Nat) (Preorder.toLE.{0} (Finset.{0} Nat) (PartialOrder.toPreorder.{0} (Finset.{0} Nat) (Finset.partialOrder.{0} Nat))) (Polynomial.support.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s)) (Polynomial.support.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) p)
+Case conversion may be inaccurate. Consider using '#align polynomial.support_scale_roots_le Polynomial.support_scaleRoots_leₓ'. -/
 theorem support_scaleRoots_le (p : R[X]) (s : R) : (scaleRoots p s).support ≤ p.support :=
   by
   intro
   simpa using left_ne_zero_of_mul
 #align polynomial.support_scale_roots_le Polynomial.support_scaleRoots_le
--/
 
 /- warning: polynomial.support_scale_roots_eq -> Polynomial.support_scaleRoots_eq is a dubious translation:
 lean 3 declaration is

10bf4f82

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -41,7 +41,7 @@ noncomputable def scaleRoots (p : R[X]) (s : R) : R[X] :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) (s : R) (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s) i) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p i) (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_4)))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p) i)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) (s : R) (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s) i) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p i) (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_4)))))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p) i)))
+  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (s : R) (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s) i) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (Polynomial.coeff.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) p i) (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_4)))))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) p) i)))
 Case conversion may be inaccurate. Consider using '#align polynomial.coeff_scale_roots Polynomial.coeff_scaleRootsₓ'. -/
 @[simp]
 theorem coeff_scaleRoots (p : R[X]) (s : R) (i : ℕ) :
@@ -89,7 +89,7 @@ theorem support_scaleRoots_le (p : R[X]) (s : R) : (scaleRoots p s).support ≤
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) {s : R}, (Membership.Mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) R (Submonoid.setLike.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))))))) s (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))))) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s)) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) {s : R}, (Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))))))) s (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))))) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s)) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p))
+  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) {s : R}, (Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))) s (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s)) (Polynomial.support.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.support_scale_roots_eq Polynomial.support_scaleRoots_eqₓ'. -/
 theorem support_scaleRoots_eq (p : R[X]) {s : R} (hs : s ∈ nonZeroDivisors R) :
     (scaleRoots p s).support = p.support :=
@@ -135,7 +135,7 @@ theorem monic_scaleRoots_iff {p : R[X]} (s : R) : Monic (scaleRoots p s) ↔ Mon
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (r : R) (s : S), Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (fun (_x : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) => S -> R) (RingHom.hasCoeToFun.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (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_4)))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (fun (_x : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) => S -> R) (RingHom.hasCoeToFun.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) f s) (Polynomial.natDegree.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) p)) (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f r p))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (r : R) (s : S), Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4))))) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Ring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))))) f s) (Polynomial.natDegree.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) p)) (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f r p))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (r : R) (s : S), Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4))))) (HPow.hPow.{u1, 0, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHPow.{u1, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) Nat (Monoid.Pow.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (MonoidWithZero.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4)))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))) f s) (Polynomial.natDegree.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) p)) (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f r p))
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mulₓ'. -/
 theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     eval₂ f (f s * r) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f r p :=
@@ -166,7 +166,7 @@ theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) {r : R} {s : S}, (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f r p) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (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_4)))))))))) -> (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (fun (_x : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) => S -> R) (RingHom.hasCoeToFun.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (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_4))))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) {r : R} {s : S}, (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f r p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))))) -> (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4)))) S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5))) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] {p : Polynomial.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))} (f : RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) {r : R} {s : S}, (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f r p) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))))) -> (Eq.{succ u1} R (Polynomial.eval₂.{u2, u1} S R (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)) f (HMul.hMul.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (instHMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonUnitalNonAssocRing.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (NonAssocRing.toNonUnitalNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (Ring.toNonAssocRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) (CommRing.toRing.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) s) _inst_4))))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S (fun (_x : S) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : S) => R) _x) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u2, u1} (RingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4)))) S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))) (RingHom.instRingHomClassRingHom.{u2, u1} S R (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S (CommRing.toCommSemiring.{u2} S _inst_5))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))) f s) r) (Polynomial.scaleRoots.{u2} S _inst_5 p s)) (OfNat.ofNat.{u1} R 0 (Zero.toOfNat0.{u1} R (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R (CommRing.toCommSemiring.{u1} R _inst_4))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zeroₓ'. -/
 theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (hr : eval₂ f r p = 0) :
     eval₂ f (f s * r) (scaleRoots p s) = 0 := by rw [scale_roots_eval₂_mul, hr, _root_.mul_zero]
@@ -183,7 +183,7 @@ theorem scaleRoots_aeval_eq_zero [Algebra S R] {p : S[X]} {r : R} {s : S} (hr :
 lean 3 declaration is
   forall {A : Type.{u1}} {K : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_3 : Field.{u2} K] {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {f : RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))}, (Function.Injective.{succ u1, succ u2} A K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) f)) -> (forall {r : A} {s : A}, (Eq.{succ u2} K (Polynomial.eval₂.{u1, u2} A K (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) f (HDiv.hDiv.{u2, u2, u2} K K K (instHDiv.{u2} K (DivInvMonoid.toHasDiv.{u2} K (DivisionRing.toDivInvMonoid.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) f r) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) f s)) p) (OfNat.ofNat.{u2} K 0 (OfNat.mk.{u2} K 0 (Zero.zero.{u2} K (MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))))))))) -> (Membership.Mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))))) s (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))) -> (Eq.{succ u2} K (Polynomial.eval₂.{u1, u2} A K (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) f (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) f r) (Polynomial.scaleRoots.{u1} A _inst_1 p s)) (OfNat.ofNat.{u2} K 0 (OfNat.mk.{u2} K 0 (Zero.zero.{u2} K (MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))))))))))
 but is expected to have type
-  forall {A : Type.{u2}} {K : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))] [_inst_3 : Field.{u1} K] {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {f : RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))}, (Function.Injective.{succ u2, succ u1} A K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))))))) f)) -> (forall {r : A} {s : A}, (Eq.{succ u1} K (Polynomial.eval₂.{u2, u1} A K (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) f (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) s) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (instHDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))))))) f r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))))))) f s)) p) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_3))))))) -> (Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))))))) s (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))))) -> (Eq.{succ u1} K (Polynomial.eval₂.{u2, u1} A K (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) f (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3))))) A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (NonAssocRing.toNonAssocSemiring.{u2} A (Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))))))) f r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_3))))))))
+  forall {A : Type.{u2}} {K : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_3 : Field.{u1} K] {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {f : RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))}, (Function.Injective.{succ u2, succ u1} A K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f)) -> (forall {r : A} {s : A}, (Eq.{succ u1} K (Polynomial.eval₂.{u2, u1} A K (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) f (HDiv.hDiv.{u1, u1, u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) s) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (instHDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toDiv.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f r) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f s)) p) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_3))))))) -> (Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) s (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) -> (Eq.{succ u1} K (Polynomial.eval₂.{u2, u1} A K (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) f (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) f r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zeroₓ'. -/
 theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+* K}
     (hf : Function.Injective f) {r s : A} (hr : eval₂ f (f r / f s) p = 0)
@@ -198,7 +198,7 @@ theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+
 lean 3 declaration is
   forall {A : Type.{u1}} {K : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : IsDomain.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] [_inst_3 : Field.{u2} K] [_inst_6 : Algebra.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))], (Function.Injective.{succ u1, succ u2} A K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) _inst_6))) -> (forall {p : Polynomial.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))} {r : A} {s : A}, (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) K (CommRing.toCommSemiring.{u1} A _inst_1) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) (Polynomial.algebraOfAlgebra.{u1, u1} A A (CommRing.toCommSemiring.{u1} A _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)) (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) K (CommRing.toCommSemiring.{u1} A _inst_1) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) (Polynomial.algebraOfAlgebra.{u1, u1} A A (CommRing.toCommSemiring.{u1} A _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)) (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) _inst_6) => (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) -> K) ([anonymous].{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) K (CommRing.toCommSemiring.{u1} A _inst_1) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) (Polynomial.algebraOfAlgebra.{u1, u1} A A (CommRing.toCommSemiring.{u1} A _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)) (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) _inst_6) (Polynomial.aeval.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) _inst_6 (HDiv.hDiv.{u2, u2, u2} K K K (instHDiv.{u2} K (DivInvMonoid.toHasDiv.{u2} K (DivisionRing.toDivInvMonoid.{u2} K (Field.toDivisionRing.{u2} K _inst_3)))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) _inst_6) r) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) _inst_6) s))) p) (OfNat.ofNat.{u2} K 0 (OfNat.mk.{u2} K 0 (Zero.zero.{u2} K (MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))))))))) -> (Membership.Mem.{u1, u1} A (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)))))) (SetLike.hasMem.{u1, u1} (Submonoid.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1)))))) A (Submonoid.setLike.{u1} A (MulZeroOneClass.toMulOneClass.{u1} A (MonoidWithZero.toMulZeroOneClass.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))))) s (nonZeroDivisors.{u1} A (Semiring.toMonoidWithZero.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))))) -> (Eq.{succ u2} K (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) K (CommRing.toCommSemiring.{u1} A _inst_1) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) (Polynomial.algebraOfAlgebra.{u1, u1} A A (CommRing.toCommSemiring.{u1} A _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)) (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) _inst_6) (fun (_x : AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) K (CommRing.toCommSemiring.{u1} A _inst_1) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) (Polynomial.algebraOfAlgebra.{u1, u1} A A (CommRing.toCommSemiring.{u1} A _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)) (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) _inst_6) => (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) -> K) ([anonymous].{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) K (CommRing.toCommSemiring.{u1} A _inst_1) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) (Polynomial.algebraOfAlgebra.{u1, u1} A A (CommRing.toCommSemiring.{u1} A _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1)) (Algebra.id.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) _inst_6) (Polynomial.aeval.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) _inst_6 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (fun (_x : RingHom.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) => A -> K) (RingHom.hasCoeToFun.{u1, u2} A K (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} K (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))) (algebraMap.{u1, u2} A K (CommRing.toCommSemiring.{u1} A _inst_1) (Ring.toSemiring.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))) _inst_6) r)) (Polynomial.scaleRoots.{u1} A _inst_1 p s)) (OfNat.ofNat.{u2} K 0 (OfNat.mk.{u2} K 0 (Zero.zero.{u2} K (MulZeroClass.toHasZero.{u2} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} K (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} K (NonAssocRing.toNonUnitalNonAssocRing.{u2} K (Ring.toNonAssocRing.{u2} K (DivisionRing.toRing.{u2} K (Field.toDivisionRing.{u2} K _inst_3))))))))))))
 but is expected to have type
-  forall {A : Type.{u2}} {K : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : IsDomain.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))] [_inst_3 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))], (Function.Injective.{succ u2, succ u1} A K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6))) -> (forall {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {r : A} {s : A}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (fun (_x : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) 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(Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) _inst_3))))))) -> (Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))))))) s (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (fun (_x : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6))))) (Polynomial.aeval.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) r)) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) _inst_3))))))))
+  forall {A : Type.{u2}} {K : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : IsDomain.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] [_inst_3 : Field.{u1} K] [_inst_6 : Algebra.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))], (Function.Injective.{succ u2, succ u1} A K (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6))) -> (forall {p : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))} {r : A} {s : A}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (fun (_x : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) 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(x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) 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(Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => 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A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) s))) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) 0 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(Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) _inst_3))))))) -> (Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) s (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (fun (_x : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6))))) (Polynomial.aeval.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) r)) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) _inst_3))))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zeroₓ'. -/
 theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
     (inj : Function.Injective (algebraMap A K)) {p : A[X]} {r s : A}
@@ -211,7 +211,7 @@ theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) (x : R) (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) f (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))))))))) -> (Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) f (Polynomial.scaleRoots.{u1} R _inst_4 p x)) (Polynomial.scaleRoots.{u2} S _inst_5 (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) f p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) f x)))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : CommRing.{u2} R] [_inst_5 : CommRing.{u1} S] (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4))) (x : R) (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))), (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))))))) f (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) _inst_5)))))) -> (Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_5))) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_5)) f (Polynomial.scaleRoots.{u2} R _inst_4 p x)) (Polynomial.scaleRoots.{u1} S _inst_5 (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_5)) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))))))) f x)))
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : CommRing.{u2} R] [_inst_5 : CommRing.{u1} S] (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (x : R) (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))), (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) f (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) p)) _inst_5)))))) -> (Eq.{succ u1} (Polynomial.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (Polynomial.map.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) f (Polynomial.scaleRoots.{u2} R _inst_4 p x)) (Polynomial.scaleRoots.{u1} S _inst_5 (Polynomial.map.{u2, u1} R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)) (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_4))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_5))))))) f x)))
 Case conversion may be inaccurate. Consider using '#align polynomial.map_scale_roots Polynomial.map_scaleRootsₓ'. -/
 theorem map_scaleRoots (p : R[X]) (x : R) (f : R →+* S) (h : f p.leadingCoeff ≠ 0) :
     (p.scaleRoots x).map f = (p.map f).scaleRoots (f x) :=

10bf4f82

bump to nightly-2023-03-16-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

8ae28b0b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Devon Tuma
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.scale_roots
-! leanprover-community/mathlib commit 40ac1b258344e0c2b4568dc37bfad937ec35a727
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Data.Polynomial.AlgebraMap
 /-!
 # Scaling the roots of a polynomial
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines `scale_roots p s` for a polynomial `p` in one variable and a ring element `s` to
 be the polynomial with root `r * s` for each root `r` of `p` and proves some basic results about it.
 -/

40ac1b25

bump to nightly-2023-03-13-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

a0c9db6f

Diff

@@ -27,29 +27,42 @@ namespace Polynomial
 
 open BigOperators Polynomial
 
+#print Polynomial.scaleRoots /-
 /-- `scale_roots p s` is a polynomial with root `r * s` for each root `r` of `p`. -/
 noncomputable def scaleRoots (p : R[X]) (s : R) : R[X] :=
   ∑ i in p.support, monomial i (p.coeff i * s ^ (p.natDegree - i))
 #align polynomial.scale_roots Polynomial.scaleRoots
+-/
 
+/- warning: polynomial.coeff_scale_roots -> Polynomial.coeff_scaleRoots is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) (s : R) (i : Nat), Eq.{succ u1} R (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s) i) (HMul.hMul.{u1, u1, u1} R R R (instHMul.{u1} R (NonUnitalNonAssocRing.toMul.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))))) (Polynomial.coeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p i) (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_4)))))) s (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) (Polynomial.natDegree.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p) i)))
+Case conversion may be inaccurate. Consider using '#align polynomial.coeff_scale_roots Polynomial.coeff_scaleRootsₓ'. -/
 @[simp]
 theorem coeff_scaleRoots (p : R[X]) (s : R) (i : ℕ) :
     (scaleRoots p s).coeff i = coeff p i * s ^ (p.natDegree - i) := by
   simp (config := { contextual := true }) [scale_roots, coeff_monomial]
 #align polynomial.coeff_scale_roots Polynomial.coeff_scaleRoots
 
+#print Polynomial.coeff_scaleRoots_natDegree /-
 theorem coeff_scaleRoots_natDegree (p : R[X]) (s : R) :
     (scaleRoots p s).coeff p.natDegree = p.leadingCoeff := by
   rw [leading_coeff, coeff_scale_roots, tsub_self, pow_zero, mul_one]
 #align polynomial.coeff_scale_roots_nat_degree Polynomial.coeff_scaleRoots_natDegree
+-/
 
+#print Polynomial.zero_scaleRoots /-
 @[simp]
 theorem zero_scaleRoots (s : R) : scaleRoots 0 s = 0 :=
   by
   ext
   simp
 #align polynomial.zero_scale_roots Polynomial.zero_scaleRoots
+-/
 
+#print Polynomial.scaleRoots_ne_zero /-
 theorem scaleRoots_ne_zero {p : R[X]} (hp : p ≠ 0) (s : R) : scaleRoots p s ≠ 0 :=
   by
   intro h
@@ -59,13 +72,22 @@ theorem scaleRoots_ne_zero {p : R[X]} (hp : p ≠ 0) (s : R) : scaleRoots p s 
   rw [coeff_scale_roots_nat_degree] at this
   contradiction
 #align polynomial.scale_roots_ne_zero Polynomial.scaleRoots_ne_zero
+-/
 
+#print Polynomial.support_scaleRoots_le /-
 theorem support_scaleRoots_le (p : R[X]) (s : R) : (scaleRoots p s).support ≤ p.support :=
   by
   intro
   simpa using left_ne_zero_of_mul
 #align polynomial.support_scale_roots_le Polynomial.support_scaleRoots_le
+-/
 
+/- warning: polynomial.support_scale_roots_eq -> Polynomial.support_scaleRoots_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_4 : CommRing.{u1} R] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) {s : R}, (Membership.mem.{u1, u1} R (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) (SetLike.instMembership.{u1, u1} (Submonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)))))) R (Submonoid.instSetLikeSubmonoid.{u1} R (MulZeroOneClass.toMulOneClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))))))) s (nonZeroDivisors.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))))) -> (Eq.{1} (Finset.{0} Nat) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Polynomial.scaleRoots.{u1} R _inst_4 p s)) (Polynomial.support.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.support_scale_roots_eq Polynomial.support_scaleRoots_eqₓ'. -/
 theorem support_scaleRoots_eq (p : R[X]) {s : R} (hs : s ∈ nonZeroDivisors R) :
     (scaleRoots p s).support = p.support :=
   le_antisymm (support_scaleRoots_le p s)
@@ -77,6 +99,7 @@ theorem support_scaleRoots_eq (p : R[X]) {s : R} (hs : s ∈ nonZeroDivisors R)
       contradiction)
 #align polynomial.support_scale_roots_eq Polynomial.support_scaleRoots_eq
 
+#print Polynomial.degree_scaleRoots /-
 @[simp]
 theorem degree_scaleRoots (p : R[X]) {s : R} : degree (scaleRoots p s) = degree p :=
   by
@@ -90,16 +113,27 @@ theorem degree_scaleRoots (p : R[X]) {s : R} : degree (scaleRoots p s) = degree
   have := leading_coeff_eq_zero.mp h
   contradiction
 #align polynomial.degree_scale_roots Polynomial.degree_scaleRoots
+-/
 
+#print Polynomial.natDegree_scaleRoots /-
 @[simp]
 theorem natDegree_scaleRoots (p : R[X]) (s : R) : natDegree (scaleRoots p s) = natDegree p := by
   simp only [nat_degree, degree_scale_roots]
 #align polynomial.nat_degree_scale_roots Polynomial.natDegree_scaleRoots
+-/
 
+#print Polynomial.monic_scaleRoots_iff /-
 theorem monic_scaleRoots_iff {p : R[X]} (s : R) : Monic (scaleRoots p s) ↔ Monic p := by
   simp only [monic, leading_coeff, nat_degree_scale_roots, coeff_scale_roots_nat_degree]
 #align polynomial.monic_scale_roots_iff Polynomial.monic_scaleRoots_iff
+-/
 
+/- warning: polynomial.scale_roots_eval₂_mul -> Polynomial.scaleRoots_eval₂_mul is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mulₓ'. -/
 theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     eval₂ f (f s * r) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f r p :=
   calc
@@ -125,15 +159,29 @@ theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     
 #align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mul
 
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+Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zeroₓ'. -/
 theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (hr : eval₂ f r p = 0) :
     eval₂ f (f s * r) (scaleRoots p s) = 0 := by rw [scale_roots_eval₂_mul, hr, _root_.mul_zero]
 #align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zero
 
+#print Polynomial.scaleRoots_aeval_eq_zero /-
 theorem scaleRoots_aeval_eq_zero [Algebra S R] {p : S[X]} {r : R} {s : S} (hr : aeval r p = 0) :
     aeval (algebraMap S R s * r) (scaleRoots p s) = 0 :=
   scaleRoots_eval₂_eq_zero (algebraMap S R) hr
 #align polynomial.scale_roots_aeval_eq_zero Polynomial.scaleRoots_aeval_eq_zero
+-/
 
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+but is expected to have type
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(Ring.toNonAssocRing.{u2} A (CommRing.toRing.{u2} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u1} K (Ring.toNonAssocRing.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_3)))))))) f r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} K 0 (Zero.toOfNat0.{u1} K (CommMonoidWithZero.toZero.{u1} K (CommGroupWithZero.toCommMonoidWithZero.{u1} K (Semifield.toCommGroupWithZero.{u1} K (Field.toSemifield.{u1} K _inst_3))))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zeroₓ'. -/
 theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+* K}
     (hf : Function.Injective f) {r s : A} (hr : eval₂ f (f r / f s) p = 0)
     (hs : s ∈ nonZeroDivisors A) : eval₂ f (f r) (scaleRoots p s) = 0 :=
@@ -143,6 +191,12 @@ theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+
   exact map_ne_zero_of_mem_nonZeroDivisors _ hf hs
 #align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero
 
+/- warning: polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero -> Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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_inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6))) -> (forall {p : Polynomial.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))} {r : A} {s : A}, (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (fun (_x : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun 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(CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) 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_inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) 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A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A 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(Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) s))) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) p) _inst_3))))))) -> (Membership.mem.{u2, u2} A (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)))))) (SetLike.instMembership.{u2, u2} (Submonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1)))))) A (Submonoid.instSetLikeSubmonoid.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))))))) s (nonZeroDivisors.{u2} A (Semiring.toMonoidWithZero.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_1))))) -> (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (fun (_x : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (SMulZeroClass.toSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toZero.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (DistribMulAction.toDistribSMul.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))))) (SMulZeroClass.toSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribSMul.toSMulZeroClass.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))))) (DistribMulAction.toDistribSMul.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))))) (Module.toDistribMulAction.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))))) (Algebra.toModule.{u2, u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (Module.toDistribMulAction.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3)))))) (Algebra.toModule.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6 (AlgHom.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6) (AlgHom.algHomClass.{u2, u2, u1} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) (Polynomial.algebraOfAlgebra.{u2, u2} A A (CommRing.toCommSemiring.{u2} A _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (Algebra.id.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) _inst_6))))) (Polynomial.aeval.{u2, u1} A ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Semifield.toDivisionSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) _inst_3))) _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} K (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))))) A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))) (RingHom.instRingHomClassRingHom.{u2, u1} A K (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} K (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3)))))))) (algebraMap.{u2, u1} A K (CommRing.toCommSemiring.{u2} A _inst_1) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_3))) _inst_6) r)) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (CommGroupWithZero.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Semifield.toCommGroupWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) (Field.toSemifield.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => K) r) (Polynomial.scaleRoots.{u2} A _inst_1 p s)) _inst_3))))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zeroₓ'. -/
 theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
     (inj : Function.Injective (algebraMap A K)) {p : A[X]} {r s : A}
     (hr : aeval (algebraMap A K r / algebraMap A K s) p = 0) (hs : s ∈ nonZeroDivisors A) :
@@ -150,6 +204,12 @@ theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
   scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero inj hr hs
 #align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero
 
+/- warning: polynomial.map_scale_roots -> Polynomial.map_scaleRoots is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_4 : CommRing.{u1} R] [_inst_5 : CommRing.{u2} S] (p : Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4))) (x : R) (f : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))), (Ne.{succ u2} S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) f (Polynomial.leadingCoeff.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) p)) (OfNat.ofNat.{u2} S 0 (OfNat.mk.{u2} S 0 (Zero.zero.{u2} S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))))))))) -> (Eq.{succ u2} (Polynomial.{u2} S (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5))) (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) f (Polynomial.scaleRoots.{u1} R _inst_4 p x)) (Polynomial.scaleRoots.{u2} S _inst_5 (Polynomial.map.{u1, u2} R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_4)) (Ring.toSemiring.{u2} S (CommRing.toRing.{u2} S _inst_5)) f p) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) (fun (_x : RingHom.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u2} S (Ring.toNonAssocRing.{u2} S (CommRing.toRing.{u2} S _inst_5)))) f x)))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u1}} [_inst_4 : CommRing.{u2} R] [_inst_5 : CommRing.{u1} S] (p : Polynomial.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4))) (x : R) (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))), (Ne.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} 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(NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))))))) f (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) (CommMonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) (CommSemiring.toCommMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) (CommRing.toCommSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (Polynomial.leadingCoeff.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) p)) _inst_5)))))) -> (Eq.{succ u1} (Polynomial.{u1} S (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_5))) (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_5)) f (Polynomial.scaleRoots.{u2} R _inst_4 p x)) (Polynomial.scaleRoots.{u1} S _inst_5 (Polynomial.map.{u2, u1} R S (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_4)) (Ring.toSemiring.{u1} S (CommRing.toRing.{u1} S _inst_5)) f p) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5)))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_4))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_5))))))) f x)))
+Case conversion may be inaccurate. Consider using '#align polynomial.map_scale_roots Polynomial.map_scaleRootsₓ'. -/
 theorem map_scaleRoots (p : R[X]) (x : R) (f : R →+* S) (h : f p.leadingCoeff ≠ 0) :
     (p.scaleRoots x).map f = (p.map f).scaleRoots (f x) :=
   by

40ac1b25

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -108,18 +108,18 @@ theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
           f (coeff p i * s ^ (p.natDegree - i)) * (f s * r) ^ i :=
       by simp [eval₂_eq_sum, sum_def]
     _ = p.support.Sum fun i => f (coeff p i * s ^ (p.natDegree - i)) * (f s * r) ^ i :=
-      Finset.sum_subset (support_scaleRoots_le p s) fun i hi hi' =>
+      (Finset.sum_subset (support_scaleRoots_le p s) fun i hi hi' =>
         by
         let this : coeff p i * s ^ (p.natDegree - i) = 0 := by simpa using hi'
-        simp [this]
+        simp [this])
     _ = p.support.Sum fun i : ℕ => f (p.coeff i) * f s ^ (p.natDegree - i + i) * r ^ i :=
-      Finset.sum_congr rfl fun i hi => by
-        simp_rw [f.map_mul, f.map_pow, pow_add, mul_pow, mul_assoc]
+      (Finset.sum_congr rfl fun i hi => by
+        simp_rw [f.map_mul, f.map_pow, pow_add, mul_pow, mul_assoc])
     _ = p.support.Sum fun i : ℕ => f s ^ p.natDegree * (f (p.coeff i) * r ^ i) :=
-      Finset.sum_congr rfl fun i hi =>
+      (Finset.sum_congr rfl fun i hi =>
         by
         rw [mul_assoc, mul_left_comm, tsub_add_cancel_of_le]
-        exact le_nat_degree_of_ne_zero (polynomial.mem_support_iff.mp hi)
+        exact le_nat_degree_of_ne_zero (polynomial.mem_support_iff.mp hi))
     _ = f s ^ p.natDegree * p.support.Sum fun i : ℕ => f (p.coeff i) * r ^ i := Finset.mul_sum.symm
     _ = f s ^ p.natDegree * eval₂ f r p := by simp [eval₂_eq_sum, sum_def]

40ac1b25

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

40ac1b25

chore(Algebra/Algebra): split Subalgebra.Basic (#12267)

This PR was supposed to be simultaneous with #12090 but I got ill last week.

This is based on seeing the import Algebra.Algebra.Subalgebra.Basic → RingTheory.Ideal.Operations on the longest pole. It feels like Ideal.Operations should not be needed to define the notion of subalgebra, only to construct some interesting examples. So I removed the import and split off anything that wouldn't fit.

The following results and their corollaries were split off:

Subalgebra.prod
Subalgebra.iSupLift
AlgHom.ker_rangeRestrict
Subalgebra.mem_of_finset_sum_eq_one_of_pow_smul_mem

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

4e9bd1d4

Diff

@@ -5,6 +5,7 @@ Authors: Anne Baanen, Devon Tuma
 -/
 import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
 import Mathlib.Algebra.Polynomial.AlgebraMap
+import Mathlib.RingTheory.Coprime.Basic
 
 #align_import ring_theory.polynomial.scale_roots from "leanprover-community/mathlib"@"40ac1b258344e0c2b4568dc37bfad937ec35a727"

40ac1b25

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

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

56e439ec

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Devon Tuma
 -/
 import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
-import Mathlib.Data.Polynomial.AlgebraMap
+import Mathlib.Algebra.Polynomial.AlgebraMap
 
 #align_import ring_theory.polynomial.scale_roots from "leanprover-community/mathlib"@"40ac1b258344e0c2b4568dc37bfad937ec35a727"

40ac1b25

chore: Rename mul-div cancellation lemmas (#11530)

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

4ea4a86a

Diff

@@ -171,7 +171,7 @@ theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : S[X]} {f : S →+
   set_option tactic.skipAssignedInstances false in
   nontriviality S using Subsingleton.eq_zero
   convert @scaleRoots_eval₂_eq_zero _ _ _ _ p f _ s hr
-  rw [← mul_div_assoc, mul_comm, mul_div_cancel]
+  rw [← mul_div_assoc, mul_comm, mul_div_cancel_right₀]
   exact map_ne_zero_of_mem_nonZeroDivisors _ hf hs
 #align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero

40ac1b25

chore: move Mathlib to v4.7.0-rc1 (#11162)

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

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

fa48894a

Diff

@@ -168,6 +168,7 @@ theorem scaleRoots_aeval_eq_zero [Algebra R A] {p : R[X]} {a : A} {r : R} (ha :
 theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : S[X]} {f : S →+* K}
     (hf : Function.Injective f) {r s : S} (hr : eval₂ f (f r / f s) p = 0)
     (hs : s ∈ nonZeroDivisors S) : eval₂ f (f r) (scaleRoots p s) = 0 := by
+  set_option tactic.skipAssignedInstances false in
   nontriviality S using Subsingleton.eq_zero
   convert @scaleRoots_eval₂_eq_zero _ _ _ _ p f _ s hr
   rw [← mul_div_assoc, mul_comm, mul_div_cancel]
@@ -227,10 +228,15 @@ lemma add_scaleRoots_of_natDegree_eq (p q : R[X]) (r : R) (h : natDegree p = nat
     r ^ (natDegree p - natDegree (p + q)) • (p + q).scaleRoots r =
       p.scaleRoots r + q.scaleRoots r := by
   ext n; simp only [coeff_smul, coeff_scaleRoots, coeff_add, smul_eq_mul,
-    mul_comm (r ^ _), mul_assoc, ← pow_add, ← h, ← add_mul, add_comm (_ - n)]
+    mul_comm (r ^ _), ← pow_add, ← h, ← add_mul, add_comm (_ - n)]
+  -- Adaptation note: v4.7.0-rc1
+  -- Previously `mul_assoc` was part of the `simp only` above, and this `rw` was not needed.
+  -- but this now causes a max rec depth error.
+  rw [mul_assoc, ← pow_add]
   cases lt_or_le (natDegree (p + q)) n with
   | inl hn => simp only [← coeff_add, coeff_eq_zero_of_natDegree_lt hn, zero_mul]
-  | inr hn => rw [tsub_add_tsub_cancel (natDegree_add_le_of_degree_le le_rfl h.ge) hn]
+  | inr hn =>
+      rw [add_comm (_ - n), tsub_add_tsub_cancel (natDegree_add_le_of_degree_le le_rfl h.ge) hn]
 
 lemma scaleRoots_dvd' (p q : R[X]) {r : R} (hr : IsUnit r)
     (hpq : p ∣ q) : p.scaleRoots r ∣ q.scaleRoots r := by
@@ -261,7 +267,7 @@ lemma isCoprime_scaleRoots (p q : R[X]) (r : R) (hr : IsUnit r) (h : IsCoprime p
     rw [e, natDegree_one]
   use s ^ natDegree (a * p) • s ^ (natDegree a + natDegree p - natDegree (a * p)) • a.scaleRoots r
   use s ^ natDegree (a * p) • s ^ (natDegree b + natDegree q - natDegree (b * q)) • b.scaleRoots r
-  simp only [smul_mul_assoc, ← mul_scaleRoots, smul_smul, Units.smul_def, mul_assoc,
+  simp only [s, smul_mul_assoc, ← mul_scaleRoots, smul_smul, Units.smul_def, mul_assoc,
     ← mul_pow, IsUnit.val_inv_mul, one_pow, mul_one, ← smul_add, one_smul, e, natDegree_one,
     one_scaleRoots, ← add_scaleRoots_of_natDegree_eq _ _ _ this, tsub_zero]
 alias _root_.IsCoprime.scaleRoots := isCoprime_scaleRoots

40ac1b25

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -256,8 +256,8 @@ lemma isCoprime_scaleRoots (p q : R[X]) (r : R) (hr : IsUnit r) (h : IsCoprime p
     IsCoprime (p.scaleRoots r) (q.scaleRoots r) := by
   obtain ⟨a, b, e⟩ := h
   let s : R := ↑hr.unit⁻¹
-  have : natDegree (a * p) = natDegree (b * q)
-  · apply natDegree_eq_of_natDegree_add_eq_zero
+  have : natDegree (a * p) = natDegree (b * q) := by
+    apply natDegree_eq_of_natDegree_add_eq_zero
     rw [e, natDegree_one]
   use s ^ natDegree (a * p) • s ^ (natDegree a + natDegree p - natDegree (a * p)) • a.scaleRoots r
   use s ^ natDegree (a * p) • s ^ (natDegree b + natDegree q - natDegree (b * q)) • b.scaleRoots r

40ac1b25

chore: Relocate big operator lemmas (#9383)

A bunch of lemmas in Algebra.BigOperators.Ring were not about rings. This PR moves them along with some lemmas from Data.Fintype.BigOperators to their correct place.

I create a new file with the content from #6605 to avoid importing Fin material in finset files as a result.

From LeanAPAP

b8dc3667

Diff

@@ -144,11 +144,10 @@ theorem scaleRoots_eval₂_mul_of_commute {p : S[X]} (f : S →+* A) (a : A) (s
       (Finset.sum_congr rfl fun i _hi => by
         simp_rw [f.map_mul, f.map_pow, pow_add, hsa.mul_pow, mul_assoc])
     _ = p.support.sum fun i : ℕ => f s ^ p.natDegree * (f (p.coeff i) * a ^ i) :=
-      (Finset.sum_congr rfl fun i hi => by
+      Finset.sum_congr rfl fun i hi => by
         rw [mul_assoc, ← map_pow, (hf _ _).left_comm, map_pow, tsub_add_cancel_of_le]
-        exact le_natDegree_of_ne_zero (Polynomial.mem_support_iff.mp hi))
-    _ = f s ^ p.natDegree * p.support.sum fun i : ℕ => f (p.coeff i) * a ^ i := Finset.mul_sum.symm
-    _ = f s ^ p.natDegree * eval₂ f a p := by simp [eval₂_eq_sum, sum_def]
+        exact le_natDegree_of_ne_zero (Polynomial.mem_support_iff.mp hi)
+    _ = f s ^ p.natDegree * eval₂ f a p := by simp [← Finset.mul_sum, eval₂_eq_sum, sum_def]
 
 theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     eval₂ f (f s * r) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f r p :=

40ac1b25

chore: Move RingTheory/NonZeroDivisors under Algebra instead. (#8685)

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

07e59b70

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Devon Tuma
 -/
-import Mathlib.RingTheory.NonZeroDivisors
+import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
 import Mathlib.Data.Polynomial.AlgebraMap
 
 #align_import ring_theory.polynomial.scale_roots from "leanprover-community/mathlib"@"40ac1b258344e0c2b4568dc37bfad937ec35a727"

40ac1b25

feat: Add lemmas about Polynomial.scaleRoots. (#8653)

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com> Co-authored-by: Eric Rodriguez <ericrboidi@gmail.com>

65fce9bb

Diff

@@ -99,6 +99,30 @@ theorem map_scaleRoots (p : R[X]) (x : R) (f : R →+* S) (h : f p.leadingCoeff
   simp [Polynomial.natDegree_map_of_leadingCoeff_ne_zero _ h]
 #align polynomial.map_scale_roots Polynomial.map_scaleRoots
 
+@[simp]
+lemma scaleRoots_C (r c : R) : (C c).scaleRoots r = C c := by
+  ext; simp
+
+@[simp]
+lemma scaleRoots_one (p : R[X]) :
+    p.scaleRoots 1 = p := by ext; simp
+
+@[simp]
+lemma scaleRoots_zero (p : R[X]) :
+    p.scaleRoots 0 = p.leadingCoeff • X ^ p.natDegree := by
+  ext n
+  simp only [coeff_scaleRoots, ge_iff_le, ne_eq, tsub_eq_zero_iff_le, not_le, zero_pow_eq, mul_ite,
+    mul_one, mul_zero, coeff_smul, coeff_X_pow, smul_eq_mul]
+  split_ifs with h₁ h₂ h₂
+  · subst h₂; rfl
+  · exact coeff_eq_zero_of_natDegree_lt (lt_of_le_of_ne h₁ (Ne.symm h₂))
+  · exact (h₁ h₂.ge).elim
+  · rfl
+
+@[simp]
+lemma one_scaleRoots (r : R) :
+    (1 : R[X]).scaleRoots r = 1 := by ext; simp
+
 end Semiring
 
 section CommSemiring
@@ -158,6 +182,91 @@ theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra R K]
   scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero inj hr hs
 #align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero
 
+@[simp]
+lemma scaleRoots_mul (p : R[X]) (r s) :
+    p.scaleRoots (r * s) = (p.scaleRoots r).scaleRoots s := by
+  ext; simp [mul_pow, mul_assoc]
+
+/-- Multiplication and `scaleRoots` commute up to a power of `r`. The factor disappears if we
+assume that the product of the leading coeffs does not vanish. See `Polynomial.mul_scaleRoots'`. -/
+lemma mul_scaleRoots (p q : R[X]) (r : R) :
+    r ^ (natDegree p + natDegree q - natDegree (p * q)) • (p * q).scaleRoots r =
+      p.scaleRoots r * q.scaleRoots r := by
+  ext n; simp only [coeff_scaleRoots, coeff_smul, smul_eq_mul]
+  trans (∑ x in Finset.antidiagonal n, coeff p x.1 * coeff q x.2) *
+    r ^ (natDegree p + natDegree q - n)
+  · rw [← coeff_mul]
+    cases lt_or_le (natDegree (p * q)) n with
+    | inl h => simp only [coeff_eq_zero_of_natDegree_lt h, zero_mul, mul_zero]
+    | inr h =>
+      rw [mul_comm, mul_assoc, ← pow_add, add_comm, tsub_add_tsub_cancel natDegree_mul_le h]
+  · rw [coeff_mul, Finset.sum_mul]
+    apply Finset.sum_congr rfl
+    simp only [Finset.mem_antidiagonal, coeff_scaleRoots, Prod.forall]
+    intros a b e
+    cases lt_or_le (natDegree p) a with
+    | inl h => simp only [coeff_eq_zero_of_natDegree_lt h, zero_mul, mul_zero]
+    | inr ha =>
+      cases lt_or_le (natDegree q) b with
+      | inl h => simp only [coeff_eq_zero_of_natDegree_lt h, zero_mul, mul_zero]
+      | inr hb =>
+        simp only [← e, mul_assoc, mul_comm (r ^ (_ - a)), ← pow_add]
+        rw [add_comm (_ - _), tsub_add_tsub_comm ha hb]
+
+lemma mul_scaleRoots' (p q : R[X]) (r : R) (h : leadingCoeff p * leadingCoeff q ≠ 0) :
+    (p * q).scaleRoots r = p.scaleRoots r * q.scaleRoots r := by
+  rw [← mul_scaleRoots, natDegree_mul' h, tsub_self, pow_zero, one_smul]
+
+lemma mul_scaleRoots_of_noZeroDivisors (p q : R[X]) (r : R) [NoZeroDivisors R] :
+    (p * q).scaleRoots r = p.scaleRoots r * q.scaleRoots r := by
+  by_cases hp : p = 0; · simp [hp]
+  by_cases hq : q = 0; · simp [hq]
+  apply mul_scaleRoots'
+  simp only [ne_eq, mul_eq_zero, leadingCoeff_eq_zero, hp, hq, or_self, not_false_eq_true]
+
+lemma add_scaleRoots_of_natDegree_eq (p q : R[X]) (r : R) (h : natDegree p = natDegree q) :
+    r ^ (natDegree p - natDegree (p + q)) • (p + q).scaleRoots r =
+      p.scaleRoots r + q.scaleRoots r := by
+  ext n; simp only [coeff_smul, coeff_scaleRoots, coeff_add, smul_eq_mul,
+    mul_comm (r ^ _), mul_assoc, ← pow_add, ← h, ← add_mul, add_comm (_ - n)]
+  cases lt_or_le (natDegree (p + q)) n with
+  | inl hn => simp only [← coeff_add, coeff_eq_zero_of_natDegree_lt hn, zero_mul]
+  | inr hn => rw [tsub_add_tsub_cancel (natDegree_add_le_of_degree_le le_rfl h.ge) hn]
+
+lemma scaleRoots_dvd' (p q : R[X]) {r : R} (hr : IsUnit r)
+    (hpq : p ∣ q) : p.scaleRoots r ∣ q.scaleRoots r := by
+  obtain ⟨a, rfl⟩ := hpq
+  rw [← ((hr.pow (natDegree p + natDegree a - natDegree (p * a))).map
+    (algebraMap R R[X])).dvd_mul_left, ← Algebra.smul_def, mul_scaleRoots]
+  exact dvd_mul_right (scaleRoots p r) (scaleRoots a r)
+
+lemma scaleRoots_dvd (p q : R[X]) {r : R} [NoZeroDivisors R] (hpq : p ∣ q) :
+    p.scaleRoots r ∣ q.scaleRoots r := by
+  obtain ⟨a, rfl⟩ := hpq
+  rw [mul_scaleRoots_of_noZeroDivisors]
+  exact dvd_mul_right (scaleRoots p r) (scaleRoots a r)
+alias _root_.Dvd.dvd.scaleRoots := scaleRoots_dvd
+
+lemma scaleRoots_dvd_iff (p q : R[X]) {r : R} (hr : IsUnit r) :
+    p.scaleRoots r ∣ q.scaleRoots r ↔ p ∣ q := by
+  refine ⟨?_ ∘ scaleRoots_dvd' _ _ (hr.unit⁻¹).isUnit, scaleRoots_dvd' p q hr⟩
+  simp [← scaleRoots_mul, scaleRoots_one]
+alias _root_.IsUnit.scaleRoots_dvd_iff := scaleRoots_dvd_iff
+
+lemma isCoprime_scaleRoots (p q : R[X]) (r : R) (hr : IsUnit r) (h : IsCoprime p q) :
+    IsCoprime (p.scaleRoots r) (q.scaleRoots r) := by
+  obtain ⟨a, b, e⟩ := h
+  let s : R := ↑hr.unit⁻¹
+  have : natDegree (a * p) = natDegree (b * q)
+  · apply natDegree_eq_of_natDegree_add_eq_zero
+    rw [e, natDegree_one]
+  use s ^ natDegree (a * p) • s ^ (natDegree a + natDegree p - natDegree (a * p)) • a.scaleRoots r
+  use s ^ natDegree (a * p) • s ^ (natDegree b + natDegree q - natDegree (b * q)) • b.scaleRoots r
+  simp only [smul_mul_assoc, ← mul_scaleRoots, smul_smul, Units.smul_def, mul_assoc,
+    ← mul_pow, IsUnit.val_inv_mul, one_pow, mul_one, ← smul_add, one_smul, e, natDegree_one,
+    one_scaleRoots, ← add_scaleRoots_of_natDegree_eq _ _ _ this, tsub_zero]
+alias _root_.IsCoprime.scaleRoots := isCoprime_scaleRoots
+
 end CommSemiring
 
 end Polynomial

40ac1b25

chore(IntegralClosure): noncommutative generalizations and golfs (#8406)

Zulip

Initially I just wanted to add more dot notations for IsIntegral and IsAlgebraic (done in #8437); then I noticed near-duplicates Algebra.isIntegral_of_finite [Field R] [Ring A] and RingHom.IsIntegral.of_finite [CommRing R] [CommRing A] so I went on to generalize the latter to cover the former, and generalized everything in the IntegralClosure file to the noncommutative case whenever possible.

In the process I noticed more golfs, which result in this PR. Most notably, isIntegral_of_mem_of_FG is now proven using Cayley-Hamilton and doesn't depend on the Noetherian case isIntegral_of_noetherian; the latter is now proven using the former. In total the golfs makes mathlib 227 lines leaner (+487 -714).

The main changes are in the single file RingTheory/IntegralClosure:

Change the definition of Algebra.IsIntegral which makes it unfold to IsIntegral rather than RingHom.IsIntegralElem because the former has much more APIs.
Fix lemma names involving is_integral which are actually about IsIntegralElem: RingHom.is_integral_map → RingHom.isIntegralElem_map RingHom.is_integral_of_mem_closure → RingHom.IsIntegralElem.of_mem_closure RingHom.is_integral_zero/one → RingHom.isIntegralElem_zero/one RingHom.is_integral_add/neg/sub/mul/of_mul_unit → RingHom.IsIntegralElem.add/neg/sub/mul/of_mul_unit
Add a lemma Algebra.IsIntegral.of_injective.
Move isIntegral_of_(submodule_)noetherian down and golf them.
Remove (Algebra.)isIntegral_of_finite that work only over fields, in favor of the more general (Algebra.)isIntegral.of_finite.
Merge duplicate lemmas isIntegral_of_isScalarTower and isIntegral_tower_top_of_isIntegral into IsIntegral.tower_top.
Golf IsIntegral.of_mem_of_fg by first proving IsIntegral.of_finite using Cayley-Hamilton.
Add a docstring mentioning the Kurosh problem at Algebra.IsIntegral.finite. The negative solution to the problem means the theorem doesn't generalize to noncommutative algebras.
Golf IsIntegral.tmul and isField_of_isIntegral_of_isField(').
Combine isIntegral_trans_aux into isIntegral_trans and golf.
Add Algebra namespace to isIntegral_sup.
rename lemmas for dot notation: RingHom.isIntegral_trans → RingHom.IsIntegral.trans RingHom.isIntegral_quotient/tower_bot/top_of_isIntegral → RingHom.IsIntegral.quotient/tower_bot/top isIntegral_of_mem_closure' → IsIntegral.of_mem_closure' (and the '' version) isIntegral_of_surjective → Algebra.isIntegral_of_surjective

The next changed file is RingTheory/Algebraic:

Rename: of_larger_base → tower_top (for consistency with IsIntegral) Algebra.isAlgebraic_of_finite → Algebra.IsAlgebraic.of_finite Algebra.isAlgebraic_trans → Algebra.IsAlgebraic.trans
Add new lemmasAlgebra.IsIntegral.isAlgebraic, isAlgebraic_algHom_iff, and Algebra.IsAlgebraic.of_injective to streamline some proofs.

The generalization from CommRing to Ring requires an additional lemma scaleRoots_eval₂_mul_of_commute in Polynomial/ScaleRoots.

A lemma Algebra.lmul_injective is added to Algebra/Bilinear (in order to golf the proof of IsIntegral.of_mem_of_fg).

In all other files, I merely fix the changed names, or use newly available dot notations.

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

8dba065d

Diff

@@ -103,28 +103,32 @@ end Semiring
 
 section CommSemiring
 
-variable [Semiring S] [CommSemiring R] [CommSemiring A] [Field K]
+variable [Semiring S] [CommSemiring R] [Semiring A] [Field K]
 
-theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
-    eval₂ f (f s * r) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f r p :=
-  calc
+theorem scaleRoots_eval₂_mul_of_commute {p : S[X]} (f : S →+* A) (a : A) (s : S)
+    (hsa : Commute (f s) a) (hf : ∀ s₁ s₂, Commute (f s₁) (f s₂)) :
+    eval₂ f (f s * a) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f a p := by
+   calc
     _ = (scaleRoots p s).support.sum fun i =>
-          f (coeff p i * s ^ (p.natDegree - i)) * (f s * r) ^ i :=
+          f (coeff p i * s ^ (p.natDegree - i)) * (f s * a) ^ i :=
       by simp [eval₂_eq_sum, sum_def]
-    _ = p.support.sum fun i => f (coeff p i * s ^ (p.natDegree - i)) * (f s * r) ^ i :=
+    _ = p.support.sum fun i => f (coeff p i * s ^ (p.natDegree - i)) * (f s * a) ^ i :=
       (Finset.sum_subset (support_scaleRoots_le p s) fun i _hi hi' => by
         let this : coeff p i * s ^ (p.natDegree - i) = 0 := by simpa using hi'
         simp [this])
-    _ = p.support.sum fun i : ℕ => f (p.coeff i) * f s ^ (p.natDegree - i + i) * r ^ i :=
+    _ = p.support.sum fun i : ℕ => f (p.coeff i) * f s ^ (p.natDegree - i + i) * a ^ i :=
       (Finset.sum_congr rfl fun i _hi => by
-        simp_rw [f.map_mul, f.map_pow, pow_add, mul_pow, mul_assoc])
-    _ = p.support.sum fun i : ℕ => f s ^ p.natDegree * (f (p.coeff i) * r ^ i) :=
+        simp_rw [f.map_mul, f.map_pow, pow_add, hsa.mul_pow, mul_assoc])
+    _ = p.support.sum fun i : ℕ => f s ^ p.natDegree * (f (p.coeff i) * a ^ i) :=
       (Finset.sum_congr rfl fun i hi => by
-        rw [mul_assoc, mul_left_comm, tsub_add_cancel_of_le]
+        rw [mul_assoc, ← map_pow, (hf _ _).left_comm, map_pow, tsub_add_cancel_of_le]
         exact le_natDegree_of_ne_zero (Polynomial.mem_support_iff.mp hi))
-    _ = f s ^ p.natDegree * p.support.sum fun i : ℕ => f (p.coeff i) * r ^ i := Finset.mul_sum.symm
-    _ = f s ^ p.natDegree * eval₂ f r p := by simp [eval₂_eq_sum, sum_def]
+    _ = f s ^ p.natDegree * p.support.sum fun i : ℕ => f (p.coeff i) * a ^ i := Finset.mul_sum.symm
+    _ = f s ^ p.natDegree * eval₂ f a p := by simp [eval₂_eq_sum, sum_def]
 
+theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
+    eval₂ f (f s * r) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f r p :=
+  scaleRoots_eval₂_mul_of_commute f r s (mul_comm _ _) fun _ _ ↦ mul_comm _ _
 #align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mul
 
 theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (hr : eval₂ f r p = 0) :
@@ -132,8 +136,10 @@ theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (h
 #align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zero
 
 theorem scaleRoots_aeval_eq_zero [Algebra R A] {p : R[X]} {a : A} {r : R} (ha : aeval a p = 0) :
-    aeval (algebraMap R A r * a) (scaleRoots p r) = 0 :=
-  scaleRoots_eval₂_eq_zero (algebraMap R A) ha
+    aeval (algebraMap R A r * a) (scaleRoots p r) = 0 := by
+  rw [aeval_def, scaleRoots_eval₂_mul_of_commute, ← aeval_def, ha, mul_zero]
+  · apply Algebra.commutes
+  · intros; rw [Commute, SemiconjBy, ← map_mul, ← map_mul, mul_comm]
 #align polynomial.scale_roots_aeval_eq_zero Polynomial.scaleRoots_aeval_eq_zero
 
 theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : S[X]} {f : S →+* K}

40ac1b25

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

@@ -16,7 +16,7 @@ be the polynomial with root `r * s` for each root `r` of `p` and proves some bas
 -/
 
 
-variable {R S A K : Type _}
+variable {R S A K : Type*}
 
 namespace Polynomial

40ac1b25

feat(RingTheory/Polynomial/ScaleRoots): reduce typeclass assumptions (#6213)

5c3c589c

Diff

@@ -16,14 +16,16 @@ be the polynomial with root `r * s` for each root `r` of `p` and proves some bas
 -/
 
 
-variable {A K R S : Type _} [CommRing A] [IsDomain A] [Field K] [CommRing R] [CommRing S]
-
-variable {M : Submonoid A}
+variable {R S A K : Type _}
 
 namespace Polynomial
 
 open BigOperators Polynomial
 
+section Semiring
+
+variable [Semiring R] [Semiring S]
+
 /-- `scaleRoots p s` is a polynomial with root `r * s` for each root `r` of `p`. -/
 noncomputable def scaleRoots (p : R[X]) (s : R) : R[X] :=
   ∑ i in p.support, monomial i (p.coeff i * s ^ (p.natDegree - i))
@@ -91,6 +93,18 @@ theorem monic_scaleRoots_iff {p : R[X]} (s : R) : Monic (scaleRoots p s) ↔ Mon
   simp only [Monic, leadingCoeff, natDegree_scaleRoots, coeff_scaleRoots_natDegree]
 #align polynomial.monic_scale_roots_iff Polynomial.monic_scaleRoots_iff
 
+theorem map_scaleRoots (p : R[X]) (x : R) (f : R →+* S) (h : f p.leadingCoeff ≠ 0) :
+    (p.scaleRoots x).map f = (p.map f).scaleRoots (f x) := by
+  ext
+  simp [Polynomial.natDegree_map_of_leadingCoeff_ne_zero _ h]
+#align polynomial.map_scale_roots Polynomial.map_scaleRoots
+
+end Semiring
+
+section CommSemiring
+
+variable [Semiring S] [CommSemiring R] [CommSemiring A] [Field K]
+
 theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
     eval₂ f (f s * r) (scaleRoots p s) = f s ^ p.natDegree * eval₂ f r p :=
   calc
@@ -117,30 +131,27 @@ theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (h
     eval₂ f (f s * r) (scaleRoots p s) = 0 := by rw [scaleRoots_eval₂_mul, hr, mul_zero]
 #align polynomial.scale_roots_eval₂_eq_zero Polynomial.scaleRoots_eval₂_eq_zero
 
-theorem scaleRoots_aeval_eq_zero [Algebra S R] {p : S[X]} {r : R} {s : S} (hr : aeval r p = 0) :
-    aeval (algebraMap S R s * r) (scaleRoots p s) = 0 :=
-  scaleRoots_eval₂_eq_zero (algebraMap S R) hr
+theorem scaleRoots_aeval_eq_zero [Algebra R A] {p : R[X]} {a : A} {r : R} (ha : aeval a p = 0) :
+    aeval (algebraMap R A r * a) (scaleRoots p r) = 0 :=
+  scaleRoots_eval₂_eq_zero (algebraMap R A) ha
 #align polynomial.scale_roots_aeval_eq_zero Polynomial.scaleRoots_aeval_eq_zero
 
-theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : A[X]} {f : A →+* K}
-    (hf : Function.Injective f) {r s : A} (hr : eval₂ f (f r / f s) p = 0)
-    (hs : s ∈ nonZeroDivisors A) : eval₂ f (f r) (scaleRoots p s) = 0 := by
+theorem scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero {p : S[X]} {f : S →+* K}
+    (hf : Function.Injective f) {r s : S} (hr : eval₂ f (f r / f s) p = 0)
+    (hs : s ∈ nonZeroDivisors S) : eval₂ f (f r) (scaleRoots p s) = 0 := by
+  nontriviality S using Subsingleton.eq_zero
   convert @scaleRoots_eval₂_eq_zero _ _ _ _ p f _ s hr
   rw [← mul_div_assoc, mul_comm, mul_div_cancel]
   exact map_ne_zero_of_mem_nonZeroDivisors _ hf hs
 #align polynomial.scale_roots_eval₂_eq_zero_of_eval₂_div_eq_zero Polynomial.scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero
 
-theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra A K]
-    (inj : Function.Injective (algebraMap A K)) {p : A[X]} {r s : A}
-    (hr : aeval (algebraMap A K r / algebraMap A K s) p = 0) (hs : s ∈ nonZeroDivisors A) :
-    aeval (algebraMap A K r) (scaleRoots p s) = 0 :=
+theorem scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero [Algebra R K]
+    (inj : Function.Injective (algebraMap R K)) {p : R[X]} {r s : R}
+    (hr : aeval (algebraMap R K r / algebraMap R K s) p = 0) (hs : s ∈ nonZeroDivisors R) :
+    aeval (algebraMap R K r) (scaleRoots p s) = 0 :=
   scaleRoots_eval₂_eq_zero_of_eval₂_div_eq_zero inj hr hs
 #align polynomial.scale_roots_aeval_eq_zero_of_aeval_div_eq_zero Polynomial.scaleRoots_aeval_eq_zero_of_aeval_div_eq_zero
 
-theorem map_scaleRoots (p : R[X]) (x : R) (f : R →+* S) (h : f p.leadingCoeff ≠ 0) :
-    (p.scaleRoots x).map f = (p.map f).scaleRoots (f x) := by
-  ext
-  simp [Polynomial.natDegree_map_of_leadingCoeff_ne_zero _ h]
-#align polynomial.map_scale_roots Polynomial.map_scaleRoots
+end CommSemiring
 
 end Polynomial

40ac1b25

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Anne Baanen, Devon Tuma
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.scale_roots
-! leanprover-community/mathlib commit 40ac1b258344e0c2b4568dc37bfad937ec35a727
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.NonZeroDivisors
 import Mathlib.Data.Polynomial.AlgebraMap
 
+#align_import ring_theory.polynomial.scale_roots from "leanprover-community/mathlib"@"40ac1b258344e0c2b4568dc37bfad937ec35a727"
+
 /-!
 # Scaling the roots of a polynomial

40ac1b25

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

@@ -101,21 +101,19 @@ theorem scaleRoots_eval₂_mul {p : S[X]} (f : S →+* R) (r : R) (s : S) :
           f (coeff p i * s ^ (p.natDegree - i)) * (f s * r) ^ i :=
       by simp [eval₂_eq_sum, sum_def]
     _ = p.support.sum fun i => f (coeff p i * s ^ (p.natDegree - i)) * (f s * r) ^ i :=
-      (Finset.sum_subset (support_scaleRoots_le p s) fun i _hi hi' =>
-        by
+      (Finset.sum_subset (support_scaleRoots_le p s) fun i _hi hi' => by
         let this : coeff p i * s ^ (p.natDegree - i) = 0 := by simpa using hi'
         simp [this])
     _ = p.support.sum fun i : ℕ => f (p.coeff i) * f s ^ (p.natDegree - i + i) * r ^ i :=
       (Finset.sum_congr rfl fun i _hi => by
         simp_rw [f.map_mul, f.map_pow, pow_add, mul_pow, mul_assoc])
     _ = p.support.sum fun i : ℕ => f s ^ p.natDegree * (f (p.coeff i) * r ^ i) :=
-      (Finset.sum_congr rfl fun i hi =>
-        by
+      (Finset.sum_congr rfl fun i hi => by
         rw [mul_assoc, mul_left_comm, tsub_add_cancel_of_le]
         exact le_natDegree_of_ne_zero (Polynomial.mem_support_iff.mp hi))
     _ = f s ^ p.natDegree * p.support.sum fun i : ℕ => f (p.coeff i) * r ^ i := Finset.mul_sum.symm
     _ = f s ^ p.natDegree * eval₂ f r p := by simp [eval₂_eq_sum, sum_def]
-    
+
 #align polynomial.scale_roots_eval₂_mul Polynomial.scaleRoots_eval₂_mul
 
 theorem scaleRoots_eval₂_eq_zero {p : S[X]} (f : S →+* R) {r : R} {s : S} (hr : eval₂ f r p = 0) :

40ac1b25

feat: Port RingTheory.Polynomial.ScaleRoots (#2841)

54ea1b19

`ring_theory.polynomial.scale_roots` ⟷ `Mathlib.RingTheory.Polynomial.ScaleRoots`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 467

ring_theory.polynomial.scale_roots ⟷ Mathlib.RingTheory.Polynomial.ScaleRoots

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 467

`ring_theory.polynomial.scale_roots` ⟷ `Mathlib.RingTheory.Polynomial.ScaleRoots`