ring_theory.polynomial.tower | 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

bb168510

(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: Kenny Lau, Yuyang Zhao
 -/
 import Algebra.Algebra.Tower
-import Data.Polynomial.AlgebraMap
+import Algebra.Polynomial.AlgebraMap
 
 #align_import ring_theory.polynomial.tower from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"

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 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yuyang Zhao
 -/
-import Mathbin.Algebra.Algebra.Tower
-import Mathbin.Data.Polynomial.AlgebraMap
+import Algebra.Algebra.Tower
+import Data.Polynomial.AlgebraMap
 
 #align_import ring_theory.polynomial.tower 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 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yuyang Zhao
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.tower
-! 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.Algebra.Algebra.Tower
 import Mathbin.Data.Polynomial.AlgebraMap
 
+#align_import ring_theory.polynomial.tower from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
 /-!
 # Algebra towers for polynomial

10bf4f82

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -42,10 +42,12 @@ variable [IsScalarTower R A B]
 
 variable {R B}
 
+#print Polynomial.aeval_map_algebraMap /-
 @[simp]
 theorem aeval_map_algebraMap (x : B) (p : R[X]) : aeval x (map (algebraMap R A) p) = aeval x p := by
   rw [aeval_def, aeval_def, eval₂_map, IsScalarTower.algebraMap_eq R A B]
 #align polynomial.aeval_map_algebra_map Polynomial.aeval_map_algebraMap
+-/
 
 end Semiring
 
@@ -57,24 +59,30 @@ variable [Algebra R A] [Algebra A B] [Algebra R B] [IsScalarTower R A B]
 
 variable {R A}
 
+#print Polynomial.aeval_algebraMap_apply /-
 theorem aeval_algebraMap_apply (x : A) (p : R[X]) :
     aeval (algebraMap A B x) p = algebraMap A B (aeval x p) := by
   rw [aeval_def, aeval_def, hom_eval₂, ← IsScalarTower.algebraMap_eq]
 #align polynomial.aeval_algebra_map_apply Polynomial.aeval_algebraMap_apply
+-/
 
+#print Polynomial.aeval_algebraMap_eq_zero_iff /-
 @[simp]
 theorem aeval_algebraMap_eq_zero_iff [NoZeroSMulDivisors A B] [Nontrivial B] (x : A) (p : R[X]) :
     aeval (algebraMap A B x) p = 0 ↔ aeval x p = 0 := by
   rw [aeval_algebra_map_apply, Algebra.algebraMap_eq_smul_one, smul_eq_zero,
     iff_false_intro (one_ne_zero' B), or_false_iff]
 #align polynomial.aeval_algebra_map_eq_zero_iff Polynomial.aeval_algebraMap_eq_zero_iff
+-/
 
 variable {B}
 
+#print Polynomial.aeval_algebraMap_eq_zero_iff_of_injective /-
 theorem aeval_algebraMap_eq_zero_iff_of_injective {x : A} {p : R[X]}
     (h : Function.Injective (algebraMap A B)) : aeval (algebraMap A B x) p = 0 ↔ aeval x p = 0 := by
   rw [aeval_algebra_map_apply, ← (algebraMap A B).map_zero, h.eq_iff]
 #align polynomial.aeval_algebra_map_eq_zero_iff_of_injective Polynomial.aeval_algebraMap_eq_zero_iff_of_injective
+-/
 
 end CommSemiring
 
@@ -88,10 +96,12 @@ section CommSemiring
 
 variable {R A} [CommSemiring R] [CommSemiring A] [Algebra R A]
 
+#print Subalgebra.aeval_coe /-
 @[simp]
 theorem aeval_coe (S : Subalgebra R A) (x : S) (p : R[X]) : aeval (x : A) p = aeval x p :=
   aeval_algebraMap_apply A x p
 #align subalgebra.aeval_coe Subalgebra.aeval_coe
+-/
 
 end CommSemiring

10bf4f82

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -26,7 +26,7 @@ When you update this file, you can also try to make a corresponding update in
 -/
 
 
-open Polynomial
+open scoped Polynomial
 
 variable (R A B : Type _)

10bf4f82

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -42,9 +42,6 @@ variable [IsScalarTower R A B]
 
 variable {R B}
 
-/- warning: polynomial.aeval_map_algebra_map -> Polynomial.aeval_map_algebraMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.aeval_map_algebra_map Polynomial.aeval_map_algebraMapₓ'. -/
 @[simp]
 theorem aeval_map_algebraMap (x : B) (p : R[X]) : aeval x (map (algebraMap R A) p) = aeval x p := by
   rw [aeval_def, aeval_def, eval₂_map, IsScalarTower.algebraMap_eq R A B]
@@ -60,17 +57,11 @@ variable [Algebra R A] [Algebra A B] [Algebra R B] [IsScalarTower R A B]
 
 variable {R A}
 
-/- warning: polynomial.aeval_algebra_map_apply -> Polynomial.aeval_algebraMap_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_apply Polynomial.aeval_algebraMap_applyₓ'. -/
 theorem aeval_algebraMap_apply (x : A) (p : R[X]) :
     aeval (algebraMap A B x) p = algebraMap A B (aeval x p) := by
   rw [aeval_def, aeval_def, hom_eval₂, ← IsScalarTower.algebraMap_eq]
 #align polynomial.aeval_algebra_map_apply Polynomial.aeval_algebraMap_apply
 
-/- warning: polynomial.aeval_algebra_map_eq_zero_iff -> Polynomial.aeval_algebraMap_eq_zero_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_eq_zero_iff Polynomial.aeval_algebraMap_eq_zero_iffₓ'. -/
 @[simp]
 theorem aeval_algebraMap_eq_zero_iff [NoZeroSMulDivisors A B] [Nontrivial B] (x : A) (p : R[X]) :
     aeval (algebraMap A B x) p = 0 ↔ aeval x p = 0 := by
@@ -80,9 +71,6 @@ theorem aeval_algebraMap_eq_zero_iff [NoZeroSMulDivisors A B] [Nontrivial B] (x
 
 variable {B}
 
-/- warning: polynomial.aeval_algebra_map_eq_zero_iff_of_injective -> Polynomial.aeval_algebraMap_eq_zero_iff_of_injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_eq_zero_iff_of_injective Polynomial.aeval_algebraMap_eq_zero_iff_of_injectiveₓ'. -/
 theorem aeval_algebraMap_eq_zero_iff_of_injective {x : A} {p : R[X]}
     (h : Function.Injective (algebraMap A B)) : aeval (algebraMap A B x) p = 0 ↔ aeval x p = 0 := by
   rw [aeval_algebra_map_apply, ← (algebraMap A B).map_zero, h.eq_iff]
@@ -100,9 +88,6 @@ section CommSemiring
 
 variable {R A} [CommSemiring R] [CommSemiring A] [Algebra R A]
 
-/- warning: subalgebra.aeval_coe -> Subalgebra.aeval_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subalgebra.aeval_coe Subalgebra.aeval_coeₓ'. -/
 @[simp]
 theorem aeval_coe (S : Subalgebra R A) (x : S) (p : R[X]) : aeval (x : A) p = aeval x p :=
   aeval_algebraMap_apply A x p

10bf4f82

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -43,10 +43,7 @@ variable [IsScalarTower R A B]
 variable {R B}
 
 /- warning: polynomial.aeval_map_algebra_map -> Polynomial.aeval_map_algebraMap is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_map_algebra_map Polynomial.aeval_map_algebraMapₓ'. -/
 @[simp]
 theorem aeval_map_algebraMap (x : B) (p : R[X]) : aeval x (map (algebraMap R A) p) = aeval x p := by
@@ -64,10 +61,7 @@ variable [Algebra R A] [Algebra A B] [Algebra R B] [IsScalarTower R A B]
 variable {R A}
 
 /- warning: polynomial.aeval_algebra_map_apply -> Polynomial.aeval_algebraMap_apply is a dubious translation:
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(Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribMulAction.toDistribSMul.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u2, max u2 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6 (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (AlgHom.algHomClass.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6))))) (Polynomial.aeval.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_apply Polynomial.aeval_algebraMap_applyₓ'. -/
 theorem aeval_algebraMap_apply (x : A) (p : R[X]) :
     aeval (algebraMap A B x) p = algebraMap A B (aeval x p) := by
@@ -75,10 +69,7 @@ theorem aeval_algebraMap_apply (x : A) (p : R[X]) :
 #align polynomial.aeval_algebra_map_apply Polynomial.aeval_algebraMap_apply
 
 /- warning: polynomial.aeval_algebra_map_eq_zero_iff -> Polynomial.aeval_algebraMap_eq_zero_iff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} (B : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (MulZeroClass.toHasZero.{u3} B (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5)))))] [_inst_9 : Nontrivial.{u3} B] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Eq.{succ u3} B (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) x)) p) (OfNat.ofNat.{u3} B 0 (OfNat.mk.{u3} B 0 (Zero.zero.{u3} B (MulZeroClass.toHasZero.{u3} B (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))))) (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (Polynomial.aeval.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))))))
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-  forall {R : Type.{u1}} {A : Type.{u3}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] [_inst_5 : Algebra.{u3, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u3, u2} R A B (Algebra.toSMul.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u1, u2} R B _inst_1 _inst_3 _inst_6)] [_inst_8 : NoZeroSMulDivisors.{u3, u2} A B (CommMonoidWithZero.toZero.{u3} A (CommSemiring.toCommMonoidWithZero.{u3} A _inst_2)) (MonoidWithZero.toZero.{u2} B (Semiring.toMonoidWithZero.{u2} B _inst_3)) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5)] [_inst_9 : Nontrivial.{u2} B] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R 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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_eq_zero_iff Polynomial.aeval_algebraMap_eq_zero_iffₓ'. -/
 @[simp]
 theorem aeval_algebraMap_eq_zero_iff [NoZeroSMulDivisors A B] [Nontrivial B] (x : A) (p : R[X]) :
@@ -90,10 +81,7 @@ theorem aeval_algebraMap_eq_zero_iff [NoZeroSMulDivisors A B] [Nontrivial B] (x
 variable {B}
 
 /- warning: polynomial.aeval_algebra_map_eq_zero_iff_of_injective -> Polynomial.aeval_algebraMap_eq_zero_iff_of_injective is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_eq_zero_iff_of_injective Polynomial.aeval_algebraMap_eq_zero_iff_of_injectiveₓ'. -/
 theorem aeval_algebraMap_eq_zero_iff_of_injective {x : A} {p : R[X]}
     (h : Function.Injective (algebraMap A B)) : aeval (algebraMap A B x) p = 0 ↔ aeval x p = 0 := by
@@ -113,10 +101,7 @@ section CommSemiring
 variable {R A} [CommSemiring R] [CommSemiring A] [Algebra R A]
 
 /- warning: subalgebra.aeval_coe -> Subalgebra.aeval_coe is a dubious translation:
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(CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u2, 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(CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))))) (Polynomial.aeval.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) x) p))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subalgebra.aeval_coe Subalgebra.aeval_coeₓ'. -/
 @[simp]
 theorem aeval_coe (S : Subalgebra R A) (x : S) (p : R[X]) : aeval (x : A) p = aeval x p :=

10bf4f82

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -46,7 +46,7 @@ variable {R B}
 lean 3 declaration is
   forall {R : Type.{u1}} (A : Type.{u2}) {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] (x : B) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u2, u2, u3} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) B _inst_2 (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u2, u2} A A _inst_2 (CommSemiring.toSemiring.{u2} A _inst_2) (Algebra.id.{u2} A _inst_2)) _inst_5) (fun (_x : AlgHom.{u2, u2, u3} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) B _inst_2 (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u2, u2} A A _inst_2 (CommSemiring.toSemiring.{u2} A _inst_2) (Algebra.id.{u2} A _inst_2)) _inst_5) => (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) -> B) ([anonymous].{u2, u2, u3} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) B _inst_2 (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u2, u2} A A _inst_2 (CommSemiring.toSemiring.{u2} A _inst_2) (Algebra.id.{u2} A _inst_2)) _inst_5) (Polynomial.aeval.{u2, u3} A B _inst_2 _inst_3 _inst_5 x) (Polynomial.map.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A _inst_2) (algebraMap.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4) p)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 x) p)
 but is expected to have type
-  forall {R : Type.{u3}} (A : Type.{u1}) {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] [_inst_5 : Algebra.{u1, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u1, u2} R A B (Algebra.toSMul.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) (Algebra.toSMul.{u1, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_3 _inst_6)] (x : B) (p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) => B) (Polynomial.map.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A _inst_2) (algebraMap.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) p)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)) _inst_5) (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (fun (_x : Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) => B) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)) _inst_5) A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B (SMulZeroClass.toSMul.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (AddMonoid.toZero.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (MonoidWithZero.toMonoid.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (Module.toDistribMulAction.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (CommSemiring.toSemiring.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2))))))) (SMulZeroClass.toSMul.{u1, u2} A B (AddMonoid.toZero.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} A B (AddMonoid.toAddZeroClass.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} A B (MonoidWithZero.toMonoid.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)))) (Module.toDistribMulAction.{u1, u2} A B (CommSemiring.toSemiring.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (Algebra.toModule.{u1, u2} A B _inst_2 _inst_3 _inst_5))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)) _inst_5) A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B (MonoidWithZero.toMonoid.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)))) (Module.toDistribMulAction.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (CommSemiring.toSemiring.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} A B (CommSemiring.toSemiring.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (Algebra.toModule.{u1, u2} A B _inst_2 _inst_3 _inst_5)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)) _inst_5) A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B (MonoidWithZero.toMonoid.{u1} A (Semiring.toMonoidWithZero.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)) (Module.toDistribMulAction.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (CommSemiring.toSemiring.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Algebra.toModule.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)))) (Module.toDistribMulAction.{u1, u2} A B (CommSemiring.toSemiring.{u1} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (Algebra.toModule.{u1, u2} A B _inst_2 _inst_3 _inst_5)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u2, max u2 u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)) _inst_5 (AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)) _inst_5) (AlgHom.algHomClass.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)) _inst_5))))) (Polynomial.aeval.{u1, u2} A B _inst_2 _inst_3 _inst_5 x) (Polynomial.map.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A _inst_2) (algebraMap.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) p)) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => B) _x) (SMulHomClass.toFunLike.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u2} R B (AddMonoid.toZero.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u2} R B (AddMonoid.toAddZeroClass.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (DistribMulAction.toDistribSMul.{u3, u2} R B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)))) (Module.toDistribMulAction.{u3, u2} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (Algebra.toModule.{u3, u2} R B _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (Algebra.toModule.{u3, u2} R B _inst_1 _inst_3 _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (Algebra.toModule.{u3, u2} R B _inst_1 _inst_3 _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u2, max u2 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6 (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (AlgHom.algHomClass.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6))))) (Polynomial.aeval.{u3, u2} R B _inst_1 _inst_3 _inst_6 x) p)
+  forall {R : Type.{u3}} (A : Type.{u1}) {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] [_inst_5 : Algebra.{u1, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u1, u2} R A B (Algebra.toSMul.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) (Algebra.toSMul.{u1, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_3 _inst_6)] (x : B) (p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) => B) (Polynomial.map.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A _inst_2) (algebraMap.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) p)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)) _inst_5) (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (fun (_x : Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) => B) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B _inst_2 (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} A A _inst_2 (CommSemiring.toSemiring.{u1} A _inst_2) (Algebra.id.{u1} A _inst_2)) _inst_5) A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) B (SMulZeroClass.toSMul.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (AddMonoid.toZero.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Polynomial.semiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u1, u1} A (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u2} R B (AddMonoid.toAddZeroClass.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (DistribMulAction.toDistribSMul.{u3, u2} R B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)))) (Module.toDistribMulAction.{u3, u2} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (Algebra.toModule.{u3, u2} R B _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (Algebra.toModule.{u3, u2} R B _inst_1 _inst_3 _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (Algebra.toModule.{u3, u2} R B _inst_1 _inst_3 _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u2, max u2 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6 (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (AlgHom.algHomClass.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6))))) (Polynomial.aeval.{u3, u2} R B _inst_1 _inst_3 _inst_6 x) p)
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_map_algebra_map Polynomial.aeval_map_algebraMapₓ'. -/
 @[simp]
 theorem aeval_map_algebraMap (x : B) (p : R[X]) : aeval x (map (algebraMap R A) p) = aeval x p := by
@@ -67,7 +67,7 @@ variable {R A}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} (B : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u3} B (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) x)) p) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (Polynomial.aeval.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] [_inst_5 : Algebra.{u1, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u1, u2} R A B (Algebra.toSMul.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) (Algebra.toSMul.{u1, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_3 _inst_6)] (x : A) (p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribMulAction.toDistribSMul.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u2, max u2 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6 (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (AlgHom.algHomClass.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6))))) (Polynomial.aeval.{u3, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6 (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A B (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (algebraMap.{u1, u2} A B _inst_2 _inst_3 _inst_5) x)) p) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A B (NonUnitalNonAssocSemiring.toMul.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (algebraMap.{u1, u2} A B _inst_2 _inst_3 _inst_5) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u3, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u1} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4 (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4 x) p))
+  forall {R : Type.{u3}} {A : Type.{u1}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] [_inst_5 : Algebra.{u1, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u1, u2} R A B (Algebra.toSMul.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) (Algebra.toSMul.{u1, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_3 _inst_6)] (x : A) (p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) 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A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (algebraMap.{u1, u2} A B _inst_2 _inst_3 _inst_5) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u3, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u1} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4 (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4 x) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_apply Polynomial.aeval_algebraMap_applyₓ'. -/
 theorem aeval_algebraMap_apply (x : A) (p : R[X]) :
     aeval (algebraMap A B x) p = algebraMap A B (aeval x p) := by
@@ -78,7 +78,7 @@ theorem aeval_algebraMap_apply (x : A) (p : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} (B : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (MulZeroClass.toHasZero.{u3} B (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5)))))] [_inst_9 : Nontrivial.{u3} B] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Eq.{succ u3} B (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) x)) p) (OfNat.ofNat.{u3} B 0 (OfNat.mk.{u3} B 0 (Zero.zero.{u3} B (MulZeroClass.toHasZero.{u3} B (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))))) (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (Polynomial.aeval.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u3}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] [_inst_5 : Algebra.{u3, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u3, u2} R A B (Algebra.toSMul.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u1, u2} R B _inst_1 _inst_3 _inst_6)] [_inst_8 : NoZeroSMulDivisors.{u3, u2} A B (CommMonoidWithZero.toZero.{u3} A (CommSemiring.toCommMonoidWithZero.{u3} A _inst_2)) (MonoidWithZero.toZero.{u2} B (Semiring.toMonoidWithZero.{u2} B _inst_3)) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5)] [_inst_9 : Nontrivial.{u2} B] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) 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(CommSemiring.toSemiring.{u3} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u1, u1, u3} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u1, u1, u3} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u3, max u3 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4 (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) _inst_2)))))
+  forall {R : Type.{u1}} {A : Type.{u3}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] [_inst_5 : Algebra.{u3, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u3, u2} R A B (Algebra.toSMul.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u1, u2} R B _inst_1 _inst_3 _inst_6)] [_inst_8 : NoZeroSMulDivisors.{u3, u2} A B (CommMonoidWithZero.toZero.{u3} A (CommSemiring.toCommMonoidWithZero.{u3} A _inst_2)) (MonoidWithZero.toZero.{u2} B (Semiring.toMonoidWithZero.{u2} B _inst_3)) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5)] [_inst_9 : Nontrivial.{u2} B] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) 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(CommSemiring.toSemiring.{u3} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u1, u1, u3} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u1, u1, u3} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u3, max u3 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4 (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_eq_zero_iff Polynomial.aeval_algebraMap_eq_zero_iffₓ'. -/
 @[simp]
 theorem aeval_algebraMap_eq_zero_iff [NoZeroSMulDivisors A B] [Nontrivial B] (x : A) (p : R[X]) :
@@ -93,7 +93,7 @@ variable {B}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] {x : A} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5))) -> (Iff (Eq.{succ u3} B (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) x)) p) (OfNat.ofNat.{u3} B 0 (OfNat.mk.{u3} B 0 (Zero.zero.{u3} B (MulZeroClass.toHasZero.{u3} B (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))))) (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (Polynomial.aeval.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))))))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u1} B] [_inst_4 : Algebra.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u1} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u1} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u2, u1} R A B (Algebra.toSMul.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4) (Algebra.toSMul.{u2, u1} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_3 _inst_6)] {x : A} {p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (algebraMap.{u2, u1} A B _inst_2 _inst_3 _inst_5))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) 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(Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribMulAction.toDistribSMul.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) 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(AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6 (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6))))) (Polynomial.aeval.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (algebraMap.{u2, u1} A B _inst_2 _inst_3 _inst_5) x)) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) _inst_3))))) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u3, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u2} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u2, max u2 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4 (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) _inst_2))))))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u1} B] [_inst_4 : Algebra.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u1} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u1} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u2, u1} R A B (Algebra.toSMul.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4) (Algebra.toSMul.{u2, u1} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_3 _inst_6)] {x : A} {p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (algebraMap.{u2, u1} A B _inst_2 _inst_3 _inst_5))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribMulAction.toDistribSMul.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6 (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6))))) (Polynomial.aeval.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (algebraMap.{u2, u1} A B _inst_2 _inst_3 _inst_5) x)) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) _inst_3))))) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u3, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u2} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u2, max u2 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4 (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_eq_zero_iff_of_injective Polynomial.aeval_algebraMap_eq_zero_iff_of_injectiveₓ'. -/
 theorem aeval_algebraMap_eq_zero_iff_of_injective {x : A} {p : R[X]}
     (h : Function.Injective (algebraMap A B)) : aeval (algebraMap A B x) p = 0 ↔ aeval x p = 0 := by
@@ -116,7 +116,7 @@ variable {R A} [CommSemiring R] [CommSemiring A] [Algebra R A]
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] (S : Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (Polynomial.aeval.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) x S))))) x)) p) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) A (HasLiftT.mk.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) A (CoeTCₓ.coe.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) A (coeBase.{succ u2, succ u2} (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) A (coeSubtype.{succ u2} A (fun (x : A) => Membership.Mem.{u2, u2} A (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (SetLike.hasMem.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) x S))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (Subalgebra.algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 S)) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (Subalgebra.algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 S)) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S)) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Subalgebra.toSemiring.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) (Subalgebra.algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 S)) (Polynomial.aeval.{u1, u2} R (coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) _inst_1 (Subalgebra.toSemiring.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3 S) x) p))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] (S : Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) 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(Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A 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_inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))))) (Polynomial.aeval.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) x) p))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] (S : Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A 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(SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) 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(CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))))) (Polynomial.aeval.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) x) p))
 Case conversion may be inaccurate. Consider using '#align subalgebra.aeval_coe Subalgebra.aeval_coeₓ'. -/
 @[simp]
 theorem aeval_coe (S : Subalgebra R A) (x : S) (p : R[X]) : aeval (x : A) p = aeval x p :=

10bf4f82

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -116,7 +116,7 @@ variable {R A} [CommSemiring R] [CommSemiring A] [Algebra R A]
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] (S : Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (x : coeSort.{succ u2, succ (succ u2)} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Subalgebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) A (Subalgebra.setLike.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) S) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} 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 but is expected to have type
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R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))))) (Polynomial.aeval.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) x) p))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] (S : Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (x : Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R 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_inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))))) (Polynomial.aeval.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.algebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) x) p))
 Case conversion may be inaccurate. Consider using '#align subalgebra.aeval_coe Subalgebra.aeval_coeₓ'. -/
 @[simp]
 theorem aeval_coe (S : Subalgebra R A) (x : S) (p : R[X]) : aeval (x : A) p = aeval x p :=

10bf4f82

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -67,7 +67,7 @@ variable {R A}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} (B : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u3} B (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) x)) p) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (Polynomial.aeval.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u1}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] [_inst_5 : Algebra.{u1, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u1, u2} R A B (Algebra.toSMul.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) (Algebra.toSMul.{u1, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_3 _inst_6)] (x : A) (p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) 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A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (algebraMap.{u1, u2} A B _inst_2 _inst_3 _inst_5) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u3, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u1} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4 (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4 x) p))
+  forall {R : Type.{u3}} {A : Type.{u1}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] [_inst_5 : Algebra.{u1, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u1, u2} R A B (Algebra.toSMul.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) (Algebra.toSMul.{u1, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_3 _inst_6)] (x : A) (p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R 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(AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R 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_inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3)) A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3) (RingHom.instRingHomClassRingHom.{u1, u2} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) (Semiring.toNonAssocSemiring.{u2} B _inst_3))))) (algebraMap.{u1, u2} A B _inst_2 _inst_3 _inst_5) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u3, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u1} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4 (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4 x) p))
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_apply Polynomial.aeval_algebraMap_applyₓ'. -/
 theorem aeval_algebraMap_apply (x : A) (p : R[X]) :
     aeval (algebraMap A B x) p = algebraMap A B (aeval x p) := by
@@ -78,7 +78,7 @@ theorem aeval_algebraMap_apply (x : A) (p : R[X]) :
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} (B : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (MulZeroClass.toHasZero.{u3} B (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5)))))] [_inst_9 : Nontrivial.{u3} B] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Eq.{succ u3} B (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) x)) p) (OfNat.ofNat.{u3} B 0 (OfNat.mk.{u3} B 0 (Zero.zero.{u3} B (MulZeroClass.toHasZero.{u3} B (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))))) (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (Polynomial.aeval.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u3}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] [_inst_5 : Algebra.{u3, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u3, u2} R A B (Algebra.toSMul.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u1, u2} R B _inst_1 _inst_3 _inst_6)] [_inst_8 : NoZeroSMulDivisors.{u3, u2} A B (CommMonoidWithZero.toZero.{u3} A (CommSemiring.toCommMonoidWithZero.{u3} A _inst_2)) (MonoidWithZero.toZero.{u2} B (Semiring.toMonoidWithZero.{u2} B _inst_3)) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5)] [_inst_9 : Nontrivial.{u2} B] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3))) (Algebra.toModule.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} 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u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u1, u1, u3} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u1, u1, u3} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u3, max u3 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4 (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) _inst_2)))))
+  forall {R : Type.{u1}} {A : Type.{u3}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] [_inst_5 : Algebra.{u3, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u3, u2} R A B (Algebra.toSMul.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u1, u2} R B _inst_1 _inst_3 _inst_6)] [_inst_8 : NoZeroSMulDivisors.{u3, u2} A B (CommMonoidWithZero.toZero.{u3} A (CommSemiring.toCommMonoidWithZero.{u3} A _inst_2)) (MonoidWithZero.toZero.{u2} B (Semiring.toMonoidWithZero.{u2} B _inst_3)) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5)] [_inst_9 : Nontrivial.{u2} B] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} 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u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u3 u1, u1, u1, u3} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u3 u1, u1, u1, u3} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, u1, u3, max u3 u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4 (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u3} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u3} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => A) p) _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_eq_zero_iff Polynomial.aeval_algebraMap_eq_zero_iffₓ'. -/
 @[simp]
 theorem aeval_algebraMap_eq_zero_iff [NoZeroSMulDivisors A B] [Nontrivial B] (x : A) (p : R[X]) :
@@ -93,7 +93,7 @@ variable {B}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] {x : A} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, (Function.Injective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5))) -> (Iff (Eq.{succ u3} B (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) x)) p) (OfNat.ofNat.{u3} B 0 (OfNat.mk.{u3} B 0 (Zero.zero.{u3} B (MulZeroClass.toHasZero.{u3} B (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))))) (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (Polynomial.aeval.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))))))
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u1} B] [_inst_4 : Algebra.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u1} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u1} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u2, u1} R A B (Algebra.toSMul.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4) (Algebra.toSMul.{u2, u1} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_3 _inst_6)] {x : A} {p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (algebraMap.{u2, u1} A B _inst_2 _inst_3 _inst_5))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) p) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) 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(AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 _inst_3 _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3)) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 _inst_3 _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6 (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6))))) (Polynomial.aeval.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 _inst_3 _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (algebraMap.{u2, u1} A B _inst_2 _inst_3 _inst_5) x)) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) p) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) p) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) p) _inst_3))))) (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u3, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u2} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u2, max u2 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4 (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) _inst_2))))))
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u1} B] [_inst_4 : Algebra.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u1} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u1} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u2, u1} R A B (Algebra.toSMul.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4) (Algebra.toSMul.{u2, u1} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u1} R B _inst_1 _inst_3 _inst_6)] {x : A} {p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)}, (Function.Injective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3))))) (algebraMap.{u2, u1} A B _inst_2 _inst_3 _inst_5))) -> (Iff (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) p) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddMonoid.toAddZeroClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))))) (DistribMulAction.toDistribSMul.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3)) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) (Semiring.toNonAssocSemiring.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_3))) (Algebra.toModule.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6 (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6))))) (Polynomial.aeval.{u3, u1} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) x) _inst_1 _inst_3 _inst_6 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u1} B _inst_3)) A B (NonUnitalNonAssocSemiring.toMul.{u2} A 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(CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1))))))) (SMulZeroClass.toSMul.{u3, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) (DistribSMul.toSMulZeroClass.{u3, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) (DistribMulAction.toDistribSMul.{u3, u2} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u2, max u2 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4 (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u3, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (CommMonoidWithZero.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) _inst_2))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_eq_zero_iff_of_injective Polynomial.aeval_algebraMap_eq_zero_iff_of_injectiveₓ'. -/
 theorem aeval_algebraMap_eq_zero_iff_of_injective {x : A} {p : R[X]}
     (h : Function.Injective (algebraMap A B)) : aeval (algebraMap A B x) p = 0 ↔ aeval x p = 0 := by

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: Kenny Lau, Yuyang Zhao
 
 ! This file was ported from Lean 3 source module ring_theory.polynomial.tower
-! leanprover-community/mathlib commit bb168510ef455e9280a152e7f31673cabd3d7496
+! 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
 /-!
 # Algebra towers for polynomial
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves some basic results about the algebra tower structure for the type `R[X]`.
 
 This structure itself is provided elsewhere as `polynomial.is_scalar_tower`

bb168510

bump to nightly-2023-03-13-18

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

66e1e587

Diff

@@ -39,6 +39,12 @@ variable [IsScalarTower R A B]
 
 variable {R B}
 
+/- warning: polynomial.aeval_map_algebra_map -> Polynomial.aeval_map_algebraMap is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (A : Type.{u2}) {B : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] (x : B) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u3} B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u2, u2, u3} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) B _inst_2 (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u2, u2} A A _inst_2 (CommSemiring.toSemiring.{u2} A _inst_2) (Algebra.id.{u2} A _inst_2)) _inst_5) (fun (_x : AlgHom.{u2, u2, u3} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) B _inst_2 (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u2, u2} A A _inst_2 (CommSemiring.toSemiring.{u2} A _inst_2) (Algebra.id.{u2} A _inst_2)) _inst_5) => (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) -> B) ([anonymous].{u2, u2, u3} A (Polynomial.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) B _inst_2 (Polynomial.semiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) _inst_3 (Polynomial.algebraOfAlgebra.{u2, u2} A A _inst_2 (CommSemiring.toSemiring.{u2} A _inst_2) (Algebra.id.{u2} A _inst_2)) _inst_5) (Polynomial.aeval.{u2, u3} A B _inst_2 _inst_3 _inst_5 x) (Polynomial.map.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A _inst_2) (algebraMap.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4) p)) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 x) p)
+but is expected to have type
+  forall {R : Type.{u3}} (A : Type.{u1}) {B : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] [_inst_5 : Algebra.{u1, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u1, u2} R A B (Algebra.toSMul.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) (Algebra.toSMul.{u1, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_3 _inst_6)] (x : B) (p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)) => B) (Polynomial.map.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} A _inst_2) (algebraMap.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) p)) (FunLike.coe.{max (succ 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(CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 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(CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3)) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u2} R B (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B _inst_3))) (Algebra.toModule.{u3, u2} R B _inst_1 _inst_3 _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u2, max u2 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6 (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (AlgHom.algHomClass.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) B _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6))))) (Polynomial.aeval.{u3, u2} R B _inst_1 _inst_3 _inst_6 x) p)
+Case conversion may be inaccurate. Consider using '#align polynomial.aeval_map_algebra_map Polynomial.aeval_map_algebraMapₓ'. -/
 @[simp]
 theorem aeval_map_algebraMap (x : B) (p : R[X]) : aeval x (map (algebraMap R A) p) = aeval x p := by
   rw [aeval_def, aeval_def, eval₂_map, IsScalarTower.algebraMap_eq R A B]
@@ -54,11 +60,23 @@ variable [Algebra R A] [Algebra A B] [Algebra R B] [IsScalarTower R A B]
 
 variable {R A}
 
+/- warning: polynomial.aeval_algebra_map_apply -> Polynomial.aeval_algebraMap_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} (B : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Eq.{succ u3} B (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) x)) p) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (Polynomial.aeval.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p))
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u1}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u3} R] [_inst_2 : CommSemiring.{u1} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2)] [_inst_5 : Algebra.{u1, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u3, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u3, u1, u2} R A B (Algebra.toSMul.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4) (Algebra.toSMul.{u1, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u3, u2} R B _inst_1 _inst_3 _inst_6)] (x : A) (p : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u3), succ u3, succ u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (fun (_x : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u3, u3, u3, u2} (AlgHom.{u3, u3, u2} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_6) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (SMulZeroClass.toSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toAddZeroClass.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R 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(Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u3, u3, u3, u1} (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2))) (Module.toDistribMulAction.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (Algebra.toModule.{u3, u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)))) (Module.toDistribMulAction.{u3, u1} R A (CommSemiring.toSemiring.{u3} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A _inst_2)))) (Algebra.toModule.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u3, u1, max u1 u3} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4 (AlgHom.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4) (AlgHom.algHomClass.{u3, u3, u1} R (Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) A _inst_1 (Polynomial.semiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (CommSemiring.toSemiring.{u1} A _inst_2) (Polynomial.algebraOfAlgebra.{u3, u3} R R _inst_1 (CommSemiring.toSemiring.{u3} R _inst_1) (Algebra.id.{u3} R _inst_1)) _inst_4))))) (Polynomial.aeval.{u3, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_4 x) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_apply Polynomial.aeval_algebraMap_applyₓ'. -/
 theorem aeval_algebraMap_apply (x : A) (p : R[X]) :
     aeval (algebraMap A B x) p = algebraMap A B (aeval x p) := by
   rw [aeval_def, aeval_def, hom_eval₂, ← IsScalarTower.algebraMap_eq]
 #align polynomial.aeval_algebra_map_apply Polynomial.aeval_algebraMap_apply
 
+/- warning: polynomial.aeval_algebra_map_eq_zero_iff -> Polynomial.aeval_algebraMap_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} (B : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Semiring.{u3} B] [_inst_4 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] [_inst_5 : Algebra.{u2, u3} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u3} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u1, u3} R B _inst_1 _inst_3 _inst_6)))))] [_inst_8 : NoZeroSMulDivisors.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (MulZeroClass.toHasZero.{u3} B (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3))) (Algebra.toModule.{u2, u3} A B _inst_2 _inst_3 _inst_5)))))] [_inst_9 : Nontrivial.{u3} B] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Eq.{succ u3} B (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (fun (_x : AlgHom.{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> B) ([anonymous].{u1, u1, u3} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) B _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.aeval.{u1, u3} R B _inst_1 _inst_3 _inst_6 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (fun (_x : RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) => A -> B) (RingHom.hasCoeToFun.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)) (Semiring.toNonAssocSemiring.{u3} B _inst_3)) (algebraMap.{u2, u3} A B _inst_2 _inst_3 _inst_5) x)) p) (OfNat.ofNat.{u3} B 0 (OfNat.mk.{u3} B 0 (Zero.zero.{u3} B (MulZeroClass.toHasZero.{u3} B (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B _inst_3)))))))) (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u2} A _inst_2) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_4) (Polynomial.aeval.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_4 x) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u3}} (B : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Semiring.{u2} B] [_inst_4 : Algebra.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] [_inst_5 : Algebra.{u3, u2} A B _inst_2 _inst_3] [_inst_6 : Algebra.{u1, u2} R B _inst_1 _inst_3] [_inst_7 : IsScalarTower.{u1, u3, u2} R A B (Algebra.toSMul.{u1, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_4) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5) (Algebra.toSMul.{u1, u2} R B _inst_1 _inst_3 _inst_6)] [_inst_8 : NoZeroSMulDivisors.{u3, u2} A B (CommMonoidWithZero.toZero.{u3} A (CommSemiring.toCommMonoidWithZero.{u3} A _inst_2)) (MonoidWithZero.toZero.{u2} B (Semiring.toMonoidWithZero.{u2} B _inst_3)) (Algebra.toSMul.{u3, u2} A B _inst_2 _inst_3 _inst_5)] [_inst_9 : Nontrivial.{u2} B] (x : A) (p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)), Iff (Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) p) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (fun (_x : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _x) (SMulHomClass.toFunLike.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (SMulZeroClass.toSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toAddZeroClass.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u1} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1))))))) (SMulZeroClass.toSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddMonoid.toZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3))))) (DistribSMul.toSMulZeroClass.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddMonoid.toAddZeroClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3))))) (DistribMulAction.toDistribSMul.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3)))) (Module.toDistribMulAction.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3))) (Algebra.toModule.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 _inst_3 _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun 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R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)))) (Module.toDistribMulAction.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_3))) (Algebra.toModule.{u1, u2} R ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 _inst_3 _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u1, u1, u2} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_3 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_6) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : A) => B) x) 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+Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_eq_zero_iff Polynomial.aeval_algebraMap_eq_zero_iffₓ'. -/
 @[simp]
 theorem aeval_algebraMap_eq_zero_iff [NoZeroSMulDivisors A B] [Nontrivial B] (x : A) (p : R[X]) :
     aeval (algebraMap A B x) p = 0 ↔ aeval x p = 0 := by
@@ -68,6 +86,12 @@ theorem aeval_algebraMap_eq_zero_iff [NoZeroSMulDivisors A B] [Nontrivial B] (x
 
 variable {B}
 
+/- warning: polynomial.aeval_algebra_map_eq_zero_iff_of_injective -> Polynomial.aeval_algebraMap_eq_zero_iff_of_injective is a dubious translation:
+lean 3 declaration is
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(CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) (CommSemiring.toCommMonoidWithZero.{u2} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) => A) p) _inst_2))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.aeval_algebra_map_eq_zero_iff_of_injective Polynomial.aeval_algebraMap_eq_zero_iff_of_injectiveₓ'. -/
 theorem aeval_algebraMap_eq_zero_iff_of_injective {x : A} {p : R[X]}
     (h : Function.Injective (algebraMap A B)) : aeval (algebraMap A B x) p = 0 ↔ aeval x p = 0 := by
   rw [aeval_algebra_map_apply, ← (algebraMap A B).map_zero, h.eq_iff]
@@ -85,6 +109,12 @@ section CommSemiring
 
 variable {R A} [CommSemiring R] [CommSemiring A] [Algebra R A]
 
+/- warning: subalgebra.aeval_coe -> Subalgebra.aeval_coe is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Semiring.toNonAssocSemiring.{u1} (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))) (Algebra.toModule.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S)))))) (Polynomial.aeval.{u2, u1} R (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) (SetLike.instMembership.{u1, u1} (Subalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3) A (Subalgebra.instSetLikeSubalgebra.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3)) x S)) _inst_1 (Subalgebra.toSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) (Subalgebra.instAlgebraSubtypeMemSubalgebraInstMembershipInstSetLikeSubalgebraToSemiring.{u2, u1} R A _inst_1 (CommSemiring.toSemiring.{u1} A _inst_2) _inst_3 S) x) p))
+Case conversion may be inaccurate. Consider using '#align subalgebra.aeval_coe Subalgebra.aeval_coeₓ'. -/
 @[simp]
 theorem aeval_coe (S : Subalgebra R A) (x : S) (p : R[X]) : aeval (x : A) p = aeval x p :=
   aeval_algebraMap_apply A x p

bb168510

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

bb168510

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: Kenny Lau, Yuyang Zhao
 -/
 import Mathlib.Algebra.Algebra.Tower
-import Mathlib.Data.Polynomial.AlgebraMap
+import Mathlib.Algebra.Polynomial.AlgebraMap
 
 #align_import ring_theory.polynomial.tower from "leanprover-community/mathlib"@"bb168510ef455e9280a152e7f31673cabd3d7496"

bb168510

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -29,11 +29,8 @@ namespace Polynomial
 section Semiring
 
 variable [CommSemiring R] [CommSemiring A] [Semiring B]
-
 variable [Algebra R A] [Algebra A B] [Algebra R B]
-
 variable [IsScalarTower R A B]
-
 variable {R B}
 
 @[simp]
@@ -51,9 +48,7 @@ end Semiring
 section CommSemiring
 
 variable [CommSemiring R] [CommSemiring A] [Semiring B]
-
 variable [Algebra R A] [Algebra A B] [Algebra R B] [IsScalarTower R A B]
-
 variable {R A}
 
 theorem aeval_algebraMap_apply (x : A) (p : R[X]) :

bb168510

feat: define Newton's method and prove decomposition as nilpotent + root (#10284)

This is just a modified version of the code provided by Antoine Chambert-Loir here: https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/jordan-chevalley.20decomposition/near/411402670

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

229b0bad

Diff

@@ -41,6 +41,11 @@ theorem aeval_map_algebraMap (x : B) (p : R[X]) : aeval x (map (algebraMap R A)
   rw [aeval_def, aeval_def, eval₂_map, IsScalarTower.algebraMap_eq R A B]
 #align polynomial.aeval_map_algebra_map Polynomial.aeval_map_algebraMap
 
+@[simp]
+lemma eval_map_algebraMap (P : R[X]) (a : A) :
+    (map (algebraMap R A) P).eval a = aeval a P := by
+  rw [← aeval_map_algebraMap (A := A), coe_aeval_eq_eval]
+
 end Semiring
 
 section CommSemiring

bb168510

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

@@ -22,7 +22,7 @@ When you update this file, you can also try to make a corresponding update in
 
 open Polynomial
 
-variable (R A B : Type _)
+variable (R A B : Type*)
 
 namespace Polynomial

bb168510

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 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau, Yuyang Zhao
-
-! This file was ported from Lean 3 source module ring_theory.polynomial.tower
-! leanprover-community/mathlib commit bb168510ef455e9280a152e7f31673cabd3d7496
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Tower
 import Mathlib.Data.Polynomial.AlgebraMap
 
+#align_import ring_theory.polynomial.tower from "leanprover-community/mathlib"@"bb168510ef455e9280a152e7f31673cabd3d7496"
+
 /-!
 # Algebra towers for polynomial

bb168510

feat: Port RingTheory.Polynomial.Tower (#2840)

Rename only.

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

59eaf443

`ring_theory.polynomial.tower` ⟷ `Mathlib.RingTheory.Polynomial.Tower`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 467

ring_theory.polynomial.tower ⟷ Mathlib.RingTheory.Polynomial.Tower

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 467

`ring_theory.polynomial.tower` ⟷ `Mathlib.RingTheory.Polynomial.Tower`