data.mv_polynomial.funext | 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

0b899341

(last sync)

chore(mv_polynomial/funext): backport golfed proof (#18839)

This proof was timing out in https://github.com/leanprover-community/mathlib4/pull/3225, so I completely rewrote it using smaller lemmas. This is the backport.

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

Diff

@@ -6,6 +6,7 @@ Authors: Johan Commelin
 import data.polynomial.ring_division
 import data.mv_polynomial.rename
 import ring_theory.polynomial.basic
+import data.mv_polynomial.polynomial
 
 /-!
 ## Function extensionality for multivariate polynomials
@@ -30,41 +31,17 @@ variables {R : Type*} [comm_ring R] [is_domain R] [infinite R]
 private lemma funext_fin {n : ℕ} {p : mv_polynomial (fin n) R}
   (h : ∀ x : fin n → R, eval x p = 0) : p = 0 :=
 begin
-  unfreezingI { induction n with n ih generalizing R },
-  { let e := (mv_polynomial.is_empty_ring_equiv R (fin 0)),
-    apply e.injective,
-    rw ring_equiv.map_zero,
-    convert h fin_zero_elim,
-    suffices : (eval₂_hom (ring_hom.id _) (is_empty.elim' fin.is_empty)) p =
-      (eval fin_zero_elim : mv_polynomial (fin 0) R →+* R) p,
-    { rw [← this],
-      simp only [coe_eval₂_hom, is_empty_ring_equiv_apply,
-        ring_equiv.trans_apply, aeval_eq_eval₂_hom],
-      congr },
-    exact eval₂_hom_congr rfl (subsingleton.elim _ _) rfl },
-  { let e := (fin_succ_equiv R n).to_ring_equiv,
-    apply e.injective,
-    simp only [ring_equiv.map_zero],
-    apply polynomial.funext,
-    intro q,
+  induction n with n ih,
+  { apply (mv_polynomial.is_empty_ring_equiv R (fin 0)).injective,
+    rw [ring_equiv.map_zero],
+    convert h _, },
+  { apply (fin_succ_equiv R n).injective,
+    simp only [alg_equiv.map_zero],
+    refine polynomial.funext (λ q, _),
     rw [polynomial.eval_zero],
-    apply ih, swap, { apply_instance },
-    intro x,
-    dsimp [e],
-    rw [fin_succ_equiv_apply],
-    calc _ = eval _ p : _
-       ... = 0 : h _,
-    { intro i, exact fin.cases (eval x q) x i },
-    apply induction_on p,
-    { intro r,
-      simp only [eval_C, polynomial.eval_C, ring_hom.coe_comp, eval₂_hom_C], },
-    { intros, simp only [*, ring_hom.map_add, polynomial.eval_add] },
-    { intros φ i hφ, simp only [*, eval_X, polynomial.eval_mul, ring_hom.map_mul, eval₂_hom_X'],
-      congr' 1,
-      by_cases hi : i = 0,
-      { subst hi, simp only [polynomial.eval_X, fin.cases_zero] },
-      { rw [← fin.succ_pred i hi], simp only [eval_X, polynomial.eval_C, fin.cases_succ] } },
-    { apply_instance, }, },
+    apply ih (λ x, _),
+    calc _ = _ : eval_polynomial_eval_fin_succ_equiv p _ _
+       ... = 0 : h _, }
 end
 
 /-- Two multivariate polynomials over an infinite integral domain are equal

da01792c

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

0b899341

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Data.Polynomial.RingDivision
-import Data.MvPolynomial.Rename
+import Algebra.Polynomial.RingDivision
+import Algebra.MvPolynomial.Rename
 import RingTheory.Polynomial.Basic
-import Data.MvPolynomial.Polynomial
+import Algebra.MvPolynomial.Polynomial
 
 #align_import data.mv_polynomial.funext from "leanprover-community/mathlib"@"0b89934139d3be96f9dab477f10c20f9f93da580"

0b899341

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -62,6 +62,8 @@ theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, ev
   apply funext_fin
   intro x
   classical
+  convert h (Function.extend f x 0)
+  simp only [eval, eval₂_hom_rename, Function.extend_comp hf]
 #align mv_polynomial.funext MvPolynomial.funext
 -/

0b899341

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -62,8 +62,6 @@ theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, ev
   apply funext_fin
   intro x
   classical
-  convert h (Function.extend f x 0)
-  simp only [eval, eval₂_hom_rename, Function.extend_comp hf]
 #align mv_polynomial.funext MvPolynomial.funext
 -/

0b899341

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.Data.Polynomial.RingDivision
-import Mathbin.Data.MvPolynomial.Rename
-import Mathbin.RingTheory.Polynomial.Basic
-import Mathbin.Data.MvPolynomial.Polynomial
+import Data.Polynomial.RingDivision
+import Data.MvPolynomial.Rename
+import RingTheory.Polynomial.Basic
+import Data.MvPolynomial.Polynomial
 
 #align_import data.mv_polynomial.funext from "leanprover-community/mathlib"@"0b89934139d3be96f9dab477f10c20f9f93da580"

0b899341

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module data.mv_polynomial.funext
-! leanprover-community/mathlib commit 0b89934139d3be96f9dab477f10c20f9f93da580
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.RingDivision
 import Mathbin.Data.MvPolynomial.Rename
 import Mathbin.RingTheory.Polynomial.Basic
 import Mathbin.Data.MvPolynomial.Polynomial
 
+#align_import data.mv_polynomial.funext from "leanprover-community/mathlib"@"0b89934139d3be96f9dab477f10c20f9f93da580"
+
 /-!
 ## Function extensionality for multivariate polynomials

0b899341

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -50,6 +50,7 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
       _ = _ := eval_polynomial_eval_fin_succ_equiv p _ _
       _ = 0 := h _
 
+#print MvPolynomial.funext /-
 /-- Two multivariate polynomials over an infinite integral domain are equal
 if they are equal upon evaluating them on an arbitrary assignment of the variables. -/
 theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, eval x p = eval x q) :
@@ -67,11 +68,14 @@ theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, ev
   convert h (Function.extend f x 0)
   simp only [eval, eval₂_hom_rename, Function.extend_comp hf]
 #align mv_polynomial.funext MvPolynomial.funext
+-/
 
+#print MvPolynomial.funext_iff /-
 theorem funext_iff {σ : Type _} {p q : MvPolynomial σ R} :
     p = q ↔ ∀ x : σ → R, eval x p = eval x q :=
   ⟨by rintro rfl <;> simp only [forall_const, eq_self_iff_true], funext⟩
 #align mv_polynomial.funext_iff MvPolynomial.funext_iff
+-/
 
 end MvPolynomial

0b899341

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -49,7 +49,6 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
     calc
       _ = _ := eval_polynomial_eval_fin_succ_equiv p _ _
       _ = 0 := h _
-      
 
 /-- Two multivariate polynomials over an infinite integral domain are equal
 if they are equal upon evaluating them on an arbitrary assignment of the variables. -/

0b899341

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -65,8 +65,8 @@ theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, ev
   apply funext_fin
   intro x
   classical
-    convert h (Function.extend f x 0)
-    simp only [eval, eval₂_hom_rename, Function.extend_comp hf]
+  convert h (Function.extend f x 0)
+  simp only [eval, eval₂_hom_rename, Function.extend_comp hf]
 #align mv_polynomial.funext MvPolynomial.funext
 
 theorem funext_iff {σ : Type _} {p q : MvPolynomial σ R} :

0b899341

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -51,9 +51,6 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
       _ = 0 := h _
       
 
-/- warning: mv_polynomial.funext -> MvPolynomial.funext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.funext MvPolynomial.funextₓ'. -/
 /-- Two multivariate polynomials over an infinite integral domain are equal
 if they are equal upon evaluating them on an arbitrary assignment of the variables. -/
 theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, eval x p = eval x q) :
@@ -72,9 +69,6 @@ theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, ev
     simp only [eval, eval₂_hom_rename, Function.extend_comp hf]
 #align mv_polynomial.funext MvPolynomial.funext
 
-/- warning: mv_polynomial.funext_iff -> MvPolynomial.funext_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.funext_iff MvPolynomial.funext_iffₓ'. -/
 theorem funext_iff {σ : Type _} {p q : MvPolynomial σ R} :
     p = q ↔ ∀ x : σ → R, eval x p = eval x q :=
   ⟨by rintro rfl <;> simp only [forall_const, eq_self_iff_true], funext⟩

0b899341

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -59,9 +59,7 @@ if they are equal upon evaluating them on an arbitrary assignment of the variabl
 theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, eval x p = eval x q) :
     p = q :=
   by
-  suffices ∀ p, (∀ x : σ → R, eval x p = 0) → p = 0
-    by
-    rw [← sub_eq_zero, this (p - q)]
+  suffices ∀ p, (∀ x : σ → R, eval x p = 0) → p = 0 by rw [← sub_eq_zero, this (p - q)];
     simp only [h, RingHom.map_sub, forall_const, sub_self]
   clear h p q
   intro p h

0b899341

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -50,13 +50,9 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
       _ = _ := eval_polynomial_eval_fin_succ_equiv p _ _
       _ = 0 := h _
       
-#align mv_polynomial.funext_fin mv_polynomial.funext_fin
 
 /- warning: mv_polynomial.funext -> MvPolynomial.funext is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.funext MvPolynomial.funextₓ'. -/
 /-- Two multivariate polynomials over an infinite integral domain are equal
 if they are equal upon evaluating them on an arbitrary assignment of the variables. -/
@@ -79,10 +75,7 @@ theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, ev
 #align mv_polynomial.funext MvPolynomial.funext
 
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(CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.funext_iff MvPolynomial.funext_iffₓ'. -/
 theorem funext_iff {σ : Type _} {p q : MvPolynomial σ R} :
     p = q ↔ ∀ x : σ → R, eval x p = eval x q :=

0b899341

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -56,7 +56,7 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, (forall (x : σ -> R), Eq.{succ u1} R (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q)) -> (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, (forall (x : σ -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, (forall (x : σ -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.funext MvPolynomial.funextₓ'. -/
 /-- Two multivariate polynomials over an infinite integral domain are equal
 if they are equal upon evaluating them on an arbitrary assignment of the variables. -/
@@ -82,7 +82,7 @@ theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, ev
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) (forall (x : σ -> R), Eq.{succ u1} R (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) (forall (x : σ -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) (forall (x : σ -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R 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(CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R 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(CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.funext_iff MvPolynomial.funext_iffₓ'. -/
 theorem funext_iff {σ : Type _} {p q : MvPolynomial σ R} :
     p = q ↔ ∀ x : σ → R, eval x p = eval x q :=

0b899341

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -56,7 +56,7 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, (forall (x : σ -> R), Eq.{succ u1} R (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q)) -> (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, (forall (x : σ -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q)
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, (forall (x : σ -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q)) -> (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.funext MvPolynomial.funextₓ'. -/
 /-- Two multivariate polynomials over an infinite integral domain are equal
 if they are equal upon evaluating them on an arbitrary assignment of the variables. -/
@@ -82,7 +82,7 @@ theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, ev
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Eq.{max (succ u2) (succ u1)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) (forall (x : σ -> R), Eq.{succ u1} R (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (coeFn.{max (succ (max u2 u1)) (succ u1), max (succ (max u2 u1)) (succ u1)} (RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : RingHom.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) -> R) (RingHom.hasCoeToFun.{max u2 u1, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) (forall (x : σ -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) (forall (x : σ -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (fun (_x : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.funext_iff MvPolynomial.funext_iffₓ'. -/
 theorem funext_iff {σ : Type _} {p q : MvPolynomial σ R} :
     p = q ↔ ∀ x : σ → R, eval x p = eval x q :=

0b899341

bump to nightly-2023-04-29-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/a4f99eae998680d3a2c240da4a2b16354c85ee49

ca3faf7a

Diff

@@ -4,13 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.funext
-! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
+! leanprover-community/mathlib commit 0b89934139d3be96f9dab477f10c20f9f93da580
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.Polynomial.RingDivision
 import Mathbin.Data.MvPolynomial.Rename
 import Mathbin.RingTheory.Polynomial.Basic
+import Mathbin.Data.MvPolynomial.Polynomial
 
 /-!
 ## Function extensionality for multivariate polynomials
@@ -36,52 +37,19 @@ variable {R : Type _} [CommRing R] [IsDomain R] [Infinite R]
 private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
     (h : ∀ x : Fin n → R, eval x p = 0) : p = 0 :=
   by
-  induction' n with n ih generalizing R
-  · let e := MvPolynomial.isEmptyRingEquiv R (Fin 0)
-    apply e.injective
+  induction' n with n ih
+  · apply (MvPolynomial.isEmptyRingEquiv R (Fin 0)).Injective
     rw [RingEquiv.map_zero]
-    convert h finZeroElim
-    suffices
-      (eval₂_hom (RingHom.id _) (IsEmpty.elim' Fin.isEmpty)) p =
-        (eval finZeroElim : MvPolynomial (Fin 0) R →+* R) p
-      by
-      rw [← this]
-      simp only [coe_eval₂_hom, is_empty_ring_equiv_apply, RingEquiv.trans_apply,
-        aeval_eq_eval₂_hom]
-      congr
-    exact eval₂_hom_congr rfl (Subsingleton.elim _ _) rfl
-  · let e := (finSuccEquiv R n).toRingEquiv
-    apply e.injective
-    simp only [RingEquiv.map_zero]
-    apply Polynomial.funext
-    intro q
+    convert h _
+  · apply (finSuccEquiv R n).Injective
+    simp only [AlgEquiv.map_zero]
+    refine' Polynomial.funext fun q => _
     rw [Polynomial.eval_zero]
-    apply ih
-    swap
-    · infer_instance
-    intro x
-    dsimp [e]
-    rw [fin_succ_equiv_apply]
+    apply ih fun x => _
     calc
-      _ = eval _ p := _
+      _ = _ := eval_polynomial_eval_fin_succ_equiv p _ _
       _ = 0 := h _
       
-    · intro i
-      exact Fin.cases (eval x q) x i
-    apply induction_on p
-    · intro r
-      simp only [eval_C, Polynomial.eval_C, RingHom.coe_comp, eval₂_hom_C]
-    · intros
-      simp only [*, RingHom.map_add, Polynomial.eval_add]
-    · intro φ i hφ
-      simp only [*, eval_X, Polynomial.eval_mul, RingHom.map_mul, eval₂_hom_X']
-      congr 1
-      by_cases hi : i = 0
-      · subst hi
-        simp only [Polynomial.eval_X, Fin.cases_zero]
-      · rw [← Fin.succ_pred i hi]
-        simp only [eval_X, Polynomial.eval_C, Fin.cases_succ]
-    · infer_instance
 #align mv_polynomial.funext_fin mv_polynomial.funext_fin
 
 /- warning: mv_polynomial.funext -> MvPolynomial.funext is a dubious translation:

86d1873c

bump to nightly-2023-04-22-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/52932b3a083d4142e78a15dc928084a22fea9ba0

21a90077

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.funext
-! leanprover-community/mathlib commit da01792ca4894d4f3a98d06b6c50455e5ed25da3
+! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.Polynomial.Basic
 /-!
 ## Function extensionality for multivariate polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we show that two multivariate polynomials over an infinite integral domain are equal
 if they are equal upon evaluating them on an arbitrary assignment of the variables.

da01792c

bump to nightly-2023-04-20-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

3940090c

Diff

@@ -81,6 +81,12 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
     · infer_instance
 #align mv_polynomial.funext_fin mv_polynomial.funext_fin
 
+/- warning: mv_polynomial.funext -> MvPolynomial.funext is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.funext MvPolynomial.funextₓ'. -/
 /-- Two multivariate polynomials over an infinite integral domain are equal
 if they are equal upon evaluating them on an arbitrary assignment of the variables. -/
 theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, eval x p = eval x q) :
@@ -101,6 +107,12 @@ theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, ev
     simp only [eval, eval₂_hom_rename, Function.extend_comp hf]
 #align mv_polynomial.funext MvPolynomial.funext
 
+/- warning: mv_polynomial.funext_iff -> MvPolynomial.funext_iff is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] [_inst_2 : IsDomain.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))] [_inst_3 : Infinite.{succ u1} R] {σ : Type.{u2}} {p : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)} {q : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)}, Iff (Eq.{max (succ u1) (succ u2)} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) p q) (forall (x : σ -> R), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) => R) p) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (RingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) 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R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHom.instRingHomClassRingHom.{max u1 u2, u1} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) R (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u2, u1} σ R (CommRing.toCommSemiring.{u1} R _inst_1)) (MvPolynomial.commSemiring.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (MvPolynomial.eval.{u1, u2} R σ (CommRing.toCommSemiring.{u1} R _inst_1) x) q))
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.funext_iff MvPolynomial.funext_iffₓ'. -/
 theorem funext_iff {σ : Type _} {p q : MvPolynomial σ R} :
     p = q ↔ ∀ x : σ → R, eval x p = eval x q :=
   ⟨by rintro rfl <;> simp only [forall_const, eq_self_iff_true], funext⟩

da01792c

bump to nightly-2023-03-08-14

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

f7af4b63

Diff

@@ -67,7 +67,7 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
       exact Fin.cases (eval x q) x i
     apply induction_on p
     · intro r
-      simp only [eval_C, Polynomial.eval_c, RingHom.coe_comp, eval₂_hom_C]
+      simp only [eval_C, Polynomial.eval_C, RingHom.coe_comp, eval₂_hom_C]
     · intros
       simp only [*, RingHom.map_add, Polynomial.eval_add]
     · intro φ i hφ
@@ -75,9 +75,9 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
       congr 1
       by_cases hi : i = 0
       · subst hi
-        simp only [Polynomial.eval_x, Fin.cases_zero]
+        simp only [Polynomial.eval_X, Fin.cases_zero]
       · rw [← Fin.succ_pred i hi]
-        simp only [eval_X, Polynomial.eval_c, Fin.cases_succ]
+        simp only [eval_X, Polynomial.eval_C, Fin.cases_succ]
     · infer_instance
 #align mv_polynomial.funext_fin mv_polynomial.funext_fin

da01792c

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

0b899341

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

@@ -3,10 +3,10 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathlib.Data.Polynomial.RingDivision
-import Mathlib.Data.MvPolynomial.Rename
+import Mathlib.Algebra.Polynomial.RingDivision
+import Mathlib.Algebra.MvPolynomial.Polynomial
+import Mathlib.Algebra.MvPolynomial.Rename
 import Mathlib.RingTheory.Polynomial.Basic
-import Mathlib.Data.MvPolynomial.Polynomial
 
 #align_import data.mv_polynomial.funext from "leanprover-community/mathlib"@"0b89934139d3be96f9dab477f10c20f9f93da580"

0b899341

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

@@ -25,7 +25,7 @@ if they are equal upon evaluating them on an arbitrary assignment of the variabl
 
 namespace MvPolynomial
 
-variable {R : Type _} [CommRing R] [IsDomain R] [Infinite R]
+variable {R : Type*} [CommRing R] [IsDomain R] [Infinite R]
 
 private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
     (h : ∀ x : Fin n → R, eval x p = 0) : p = 0 := by
@@ -43,7 +43,7 @@ private theorem funext_fin {n : ℕ} {p : MvPolynomial (Fin n) R}
 
 /-- Two multivariate polynomials over an infinite integral domain are equal
 if they are equal upon evaluating them on an arbitrary assignment of the variables. -/
-theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, eval x p = eval x q) :
+theorem funext {σ : Type*} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, eval x p = eval x q) :
     p = q := by
   suffices ∀ p, (∀ x : σ → R, eval x p = 0) → p = 0 by
     rw [← sub_eq_zero, this (p - q)]
@@ -59,7 +59,7 @@ theorem funext {σ : Type _} {p q : MvPolynomial σ R} (h : ∀ x : σ → R, ev
     simp only [eval, eval₂Hom_rename, Function.extend_comp hf]
 #align mv_polynomial.funext MvPolynomial.funext
 
-theorem funext_iff {σ : Type _} {p q : MvPolynomial σ R} :
+theorem funext_iff {σ : Type*} {p q : MvPolynomial σ R} :
     p = q ↔ ∀ x : σ → R, eval x p = eval x q :=
   ⟨by rintro rfl; simp only [forall_const, eq_self_iff_true], funext⟩
 #align mv_polynomial.funext_iff MvPolynomial.funext_iff

0b899341

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module data.mv_polynomial.funext
-! leanprover-community/mathlib commit 0b89934139d3be96f9dab477f10c20f9f93da580
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.RingDivision
 import Mathlib.Data.MvPolynomial.Rename
 import Mathlib.RingTheory.Polynomial.Basic
 import Mathlib.Data.MvPolynomial.Polynomial
 
+#align_import data.mv_polynomial.funext from "leanprover-community/mathlib"@"0b89934139d3be96f9dab477f10c20f9f93da580"
+
 /-!
 ## Function extensionality for multivariate polynomials

0b899341

chore: forward-port backports (#3752)

data.mv_polynomial.basic, data.mv_polynomial.funext: leanprover-community/mathlib#18839
category_theory.limits.preserves.finite, category_theory.preadditive.projective: leanprover-community/mathlib#18890
category_theory.abelian.basic, category_theory.abelian.opposite: leanprover-community/mathlib#18740
topology.category.Top.limits.basic: leanprover-community/mathlib#18871. Note that this does not show a useful diff on the dashboard pages as file splits aren't tracked well by git.

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

4f474208

Diff

@@ -4,14 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.funext
-! leanprover-community/mathlib commit da01792ca4894d4f3a98d06b6c50455e5ed25da3
+! leanprover-community/mathlib commit 0b89934139d3be96f9dab477f10c20f9f93da580
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathlib.Data.Polynomial.RingDivision
 import Mathlib.Data.MvPolynomial.Rename
-import Mathlib.Data.MvPolynomial.Polynomial
 import Mathlib.RingTheory.Polynomial.Basic
+import Mathlib.Data.MvPolynomial.Polynomial
 
 /-!
 ## Function extensionality for multivariate polynomials

da01792c

feat: port Data.MvPolynomial.Funext (#3225)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>

db5f318e

`data.mv_polynomial.funext` ⟷ `Mathlib.Data.MvPolynomial.Funext`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 536

data.mv_polynomial.funext ⟷ Mathlib.Data.MvPolynomial.Funext

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 536

`data.mv_polynomial.funext` ⟷ `Mathlib.Data.MvPolynomial.Funext`