ring_theory.mv_polynomial.basic | 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

2f5b500a

(last sync)

fix(data/mv_polynomial): add missing decidable_eq arguments to lemmas (#18848)

This does not change the type of any definitions; the effect of this PR is to make the statement of the lemmas syntactically more general.

To ensure this catches them all, this removes open_locale classical from the beginning of every file in data/mv_polynomial and ring_theory/mv_polynomial.

For definitions which bake in a classical.dec_eq assumption, this adds a lemma proven by convert rfl that unfolds them to a version with an arbitrary decidable_eq instance, following a pattern established elsewhere.

Unlike previous refactors of this style this doesn't seemed to have helped any downstream proofs much.

Diff

@@ -39,8 +39,6 @@ Generalise to noncommutative (semi)rings
 
 noncomputable theory
 
-open_locale classical
-
 open set linear_map submodule
 open_locale big_operators polynomial
 
@@ -99,10 +97,10 @@ begin
   refl
 end
 
-lemma mem_restrict_degree_iff_sup (p : mv_polynomial σ R) (n : ℕ) :
+lemma mem_restrict_degree_iff_sup [decidable_eq σ] (p : mv_polynomial σ R) (n : ℕ) :
   p ∈ restrict_degree σ R n ↔ ∀i, p.degrees.count i ≤ n :=
 begin
-  simp only [mem_restrict_degree, degrees, multiset.count_finset_sup, finsupp.count_to_multiset,
+  simp only [mem_restrict_degree, degrees_def, multiset.count_finset_sup, finsupp.count_to_multiset,
     finset.sup_le_iff],
   exact ⟨assume h n s hs, h s hs n, assume h s hs n, h n s hs⟩
 end

019ead10

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

2f5b500a

bump to nightly-2024-04-07-08

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

b03b8656

Diff

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
 import Algebra.CharP.Basic
-import Data.Polynomial.AlgebraMap
-import Data.MvPolynomial.Degrees
+import Algebra.Polynomial.AlgebraMap
+import Algebra.MvPolynomial.Degrees
 import LinearAlgebra.FinsuppVectorSpace
 
 #align_import ring_theory.mv_polynomial.basic from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"

2f5b500a

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -5,7 +5,7 @@ Authors: Johannes Hölzl
 -/
 import Algebra.CharP.Basic
 import Data.Polynomial.AlgebraMap
-import Data.MvPolynomial.Variables
+import Data.MvPolynomial.Degrees
 import LinearAlgebra.FinsuppVectorSpace
 
 #align_import ring_theory.mv_polynomial.basic from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"

2f5b500a

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) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Mathbin.Algebra.CharP.Basic
-import Mathbin.Data.Polynomial.AlgebraMap
-import Mathbin.Data.MvPolynomial.Variables
-import Mathbin.LinearAlgebra.FinsuppVectorSpace
+import Algebra.CharP.Basic
+import Data.Polynomial.AlgebraMap
+import Data.MvPolynomial.Variables
+import LinearAlgebra.FinsuppVectorSpace
 
 #align_import ring_theory.mv_polynomial.basic from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"

2f5b500a

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) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module ring_theory.mv_polynomial.basic
-! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.CharP.Basic
 import Mathbin.Data.Polynomial.AlgebraMap
 import Mathbin.Data.MvPolynomial.Variables
 import Mathbin.LinearAlgebra.FinsuppVectorSpace
 
+#align_import ring_theory.mv_polynomial.basic from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
+
 /-!
 # Multivariate polynomials over commutative rings

2f5b500a

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -63,6 +63,7 @@ end CharP
 
 section Homomorphism
 
+#print MvPolynomial.mapRange_eq_map /-
 theorem mapRange_eq_map {R S : Type _} [CommRing R] [CommRing S] (p : MvPolynomial σ R)
     (f : R →+* S) : Finsupp.mapRange f f.map_zero p = map f p :=
   by
@@ -73,6 +74,7 @@ theorem mapRange_eq_map {R S : Type _} [CommRing R] [CommRing S] (p : MvPolynomi
   rw [map_monomial, ← single_eq_monomial, Finsupp.mapRange_single, single_eq_monomial,
     f.coe_add_monoid_hom]
 #align mv_polynomial.map_range_eq_map MvPolynomial.mapRange_eq_map
+-/
 
 end Homomorphism
 
@@ -132,11 +134,13 @@ def basisMonomials : Basis (σ →₀ ℕ) R (MvPolynomial σ R) :=
 #align mv_polynomial.basis_monomials MvPolynomial.basisMonomials
 -/
 
+#print MvPolynomial.coe_basisMonomials /-
 @[simp]
 theorem coe_basisMonomials :
     (basisMonomials σ R : (σ →₀ ℕ) → MvPolynomial σ R) = fun s => monomial s 1 :=
   rfl
 #align mv_polynomial.coe_basis_monomials MvPolynomial.coe_basisMonomials
+-/
 
 #print MvPolynomial.linearIndependent_X /-
 theorem linearIndependent_X : LinearIndependent R (X : σ → MvPolynomial σ R) :=
@@ -159,10 +163,12 @@ noncomputable def basisMonomials : Basis ℕ R R[X] :=
 #align polynomial.basis_monomials Polynomial.basisMonomials
 -/
 
+#print Polynomial.coe_basisMonomials /-
 @[simp]
 theorem coe_basisMonomials : (basisMonomials R : ℕ → R[X]) = fun s => monomial s 1 :=
   funext fun n => ofFinsupp_single _ _
 #align polynomial.coe_basis_monomials Polynomial.coe_basisMonomials
+-/
 
 end Polynomial

2f5b500a

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -81,7 +81,7 @@ section Degree
 #print MvPolynomial.restrictTotalDegree /-
 /-- The submodule of polynomials of total degree less than or equal to `m`.-/
 def restrictTotalDegree : Submodule R (MvPolynomial σ R) :=
-  Finsupp.supported _ _ { n | (n.Sum fun n e => e) ≤ m }
+  Finsupp.supported _ _ {n | (n.Sum fun n e => e) ≤ m}
 #align mv_polynomial.restrict_total_degree MvPolynomial.restrictTotalDegree
 -/
 
@@ -89,7 +89,7 @@ def restrictTotalDegree : Submodule R (MvPolynomial σ R) :=
 /-- The submodule of polynomials such that the degree with respect to each individual variable is
 less than or equal to `m`.-/
 def restrictDegree (m : ℕ) : Submodule R (MvPolynomial σ R) :=
-  Finsupp.supported _ _ { n | ∀ i, n i ≤ m }
+  Finsupp.supported _ _ {n | ∀ i, n i ≤ m}
 #align mv_polynomial.restrict_degree MvPolynomial.restrictDegree
 -/

2f5b500a

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -46,7 +46,7 @@ noncomputable section
 
 open Set LinearMap Submodule
 
-open BigOperators Polynomial
+open scoped BigOperators Polynomial
 
 universe u v

2f5b500a

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -63,9 +63,6 @@ end CharP
 
 section Homomorphism
 
-/- warning: mv_polynomial.map_range_eq_map -> MvPolynomial.mapRange_eq_map is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_range_eq_map MvPolynomial.mapRange_eq_mapₓ'. -/
 theorem mapRange_eq_map {R S : Type _} [CommRing R] [CommRing S] (p : MvPolynomial σ R)
     (f : R →+* S) : Finsupp.mapRange f f.map_zero p = map f p :=
   by
@@ -135,9 +132,6 @@ def basisMonomials : Basis (σ →₀ ℕ) R (MvPolynomial σ R) :=
 #align mv_polynomial.basis_monomials MvPolynomial.basisMonomials
 -/
 
-/- warning: mv_polynomial.coe_basis_monomials -> MvPolynomial.coe_basisMonomials is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_basis_monomials MvPolynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials :
     (basisMonomials σ R : (σ →₀ ℕ) → MvPolynomial σ R) = fun s => monomial s 1 :=
@@ -165,9 +159,6 @@ noncomputable def basisMonomials : Basis ℕ R R[X] :=
 #align polynomial.basis_monomials Polynomial.basisMonomials
 -/
 
-/- warning: polynomial.coe_basis_monomials -> Polynomial.coe_basisMonomials is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.coe_basis_monomials Polynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials : (basisMonomials R : ℕ → R[X]) = fun s => monomial s 1 :=
   funext fun n => ofFinsupp_single _ _

2f5b500a

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -64,10 +64,7 @@ end CharP
 section Homomorphism
 
 /- warning: mv_polynomial.map_range_eq_map -> MvPolynomial.mapRange_eq_map is a dubious translation:
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(MvPolynomial.map.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_2) (CommRing.toCommSemiring.{u1} S _inst_3) f) p)
+<too large>
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_range_eq_map MvPolynomial.mapRange_eq_mapₓ'. -/
 theorem mapRange_eq_map {R S : Type _} [CommRing R] [CommRing S] (p : MvPolynomial σ R)
     (f : R →+* S) : Finsupp.mapRange f f.map_zero p = map f p :=
@@ -139,10 +136,7 @@ def basisMonomials : Basis (σ →₀ ℕ) R (MvPolynomial σ R) :=
 -/
 
 /- warning: mv_polynomial.coe_basis_monomials -> MvPolynomial.coe_basisMonomials is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_basis_monomials MvPolynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials :
@@ -172,10 +166,7 @@ noncomputable def basisMonomials : Basis ℕ R R[X] :=
 -/
 
 /- warning: polynomial.coe_basis_monomials -> Polynomial.coe_basisMonomials is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_basis_monomials Polynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials : (basisMonomials R : ℕ → R[X]) = fun s => monomial s 1 :=

2f5b500a

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -142,7 +142,7 @@ def basisMonomials : Basis (σ →₀ ℕ) R (MvPolynomial σ R) :=
 lean 3 declaration is
   forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommRing.{u2} R], Eq.{max (succ u1) (succ u2)} ((fun (_x : Basis.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) => (Finsupp.{u1, 0} σ Nat Nat.hasZero) -> (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (coeFn.{max (succ u1) (succ u2) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (Basis.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (fun (_x : Basis.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) => (Finsupp.{u1, 0} σ Nat Nat.hasZero) -> (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1))) (FunLike.hasCoeToFun.{max (succ u1) (succ u2) (succ (max u1 u2)), succ u1, succ (max u1 u2)} (Basis.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Finsupp.{u1, 0} σ Nat Nat.hasZero) (fun (_x : Finsupp.{u1, 0} σ Nat Nat.hasZero) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Basis.funLike.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (fun (s : Finsupp.{u1, 0} σ Nat Nat.hasZero) => coeFn.{max (succ u2) (succ (max u1 u2)), max (succ u2) (succ (max u1 u2))} (LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => R -> (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.monomial.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))
 but is expected to have type
-  forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommRing.{u2} R], Eq.{max (succ u1) (succ u2)} (forall (a : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (Basis.{u1, u2, max u2 u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (Basis.funLike.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (fun (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.monomial.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
+  forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommRing.{u2} R], Eq.{max (succ u1) (succ u2)} (forall (a : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (Basis.{u1, u2, max u2 u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (Basis.funLike.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (fun (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.monomial.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_basis_monomials MvPolynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials :
@@ -175,7 +175,7 @@ noncomputable def basisMonomials : Basis ℕ R R[X] :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} ((fun (_x : Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => Nat -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.basisMonomials.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => Nat -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (FunLike.hasCoeToFun.{succ u1, 1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) Nat (fun (_x : Nat) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.funLike.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.basisMonomials.{u1} R _inst_1)) (fun (s : Nat) => coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) s) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) s) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (forall (a : Nat), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (FunLike.coe.{succ u1, 1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) Nat (fun (_x : Nat) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (Basis.funLike.{0, u1, u1} Nat R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.basisMonomials.{u1} R _inst_1)) (fun (s : Nat) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) s) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_basis_monomials Polynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials : (basisMonomials R : ℕ → R[X]) = fun s => monomial s 1 :=

2f5b500a

bump to nightly-2023-05-22-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

a4206c98

Diff

@@ -119,12 +119,7 @@ theorem mem_restrictDegree (p : MvPolynomial σ R) (n : ℕ) :
 #align mv_polynomial.mem_restrict_degree MvPolynomial.mem_restrictDegree
 -/
 
-/- warning: mv_polynomial.mem_restrict_degree_iff_sup -> MvPolynomial.mem_restrictDegree_iff_sup is a dubious translation:
-lean 3 declaration is
-  forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (p : MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (n : Nat), Iff (Membership.Mem.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.setLike.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) p (MvPolynomial.restrictDegree.{u1, u2} σ R _inst_1 n)) (forall (i : σ), LE.le.{0} Nat Nat.hasLe (Multiset.count.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b) i (MvPolynomial.degrees.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) p)) n)
-but is expected to have type
-  forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (_inst_2 : MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (p : Nat), Iff (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.setLike.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) _inst_2 (MvPolynomial.restrictDegree.{u1, u2} σ R _inst_1 p)) (forall (i : σ), LE.le.{0} Nat instLENat (Multiset.count.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) i (MvPolynomial.degrees.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) _inst_2)) p)
-Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_restrict_degree_iff_sup MvPolynomial.mem_restrictDegree_iff_supₓ'. -/
+#print MvPolynomial.mem_restrictDegree_iff_sup /-
 theorem mem_restrictDegree_iff_sup [DecidableEq σ] (p : MvPolynomial σ R) (n : ℕ) :
     p ∈ restrictDegree σ R n ↔ ∀ i, p.degrees.count i ≤ n :=
   by
@@ -132,6 +127,7 @@ theorem mem_restrictDegree_iff_sup [DecidableEq σ] (p : MvPolynomial σ R) (n :
     Finset.sup_le_iff]
   exact ⟨fun h n s hs => h s hs n, fun h s hs n => h n s hs⟩
 #align mv_polynomial.mem_restrict_degree_iff_sup MvPolynomial.mem_restrictDegree_iff_sup
+-/
 
 variable (σ R)

2f5b500a

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -67,7 +67,7 @@ section Homomorphism
 lean 3 declaration is
   forall (σ : Type.{u1}) {R : Type.{u2}} {S : Type.{u3}} [_inst_2 : CommRing.{u2} R] [_inst_3 : CommRing.{u3} S] (p : MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (f : RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))), Eq.{max (succ u1) (succ u3)} (Finsupp.{u1, u3} (Finsupp.{u1, 0} σ Nat Nat.hasZero) S (MulZeroClass.toHasZero.{u3} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3))))))) (Finsupp.mapRange.{u1, u2, u3} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R S (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))) (MulZeroClass.toHasZero.{u3} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))) (fun (_x : RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))) => R -> S) (RingHom.hasCoeToFun.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))) f) (RingHom.map_zero.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3))) f) p) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (MvPolynomial.commSemiring.{u3, u1} S σ (CommRing.toCommSemiring.{u3} S _inst_3))))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (MvPolynomial.commSemiring.{u3, u1} S σ (CommRing.toCommSemiring.{u3} S _inst_3))))) => (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) -> (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3))) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (MvPolynomial.commSemiring.{u3, u1} S σ (CommRing.toCommSemiring.{u3} S _inst_3))))) (MvPolynomial.map.{u2, u3, u1} R S σ (CommRing.toCommSemiring.{u2} R _inst_2) (CommRing.toCommSemiring.{u3} S _inst_3) f) p)
 but is expected to have type
-  forall (σ : Type.{u3}) {R : Type.{u2}} {S : Type.{u1}} [_inst_2 : CommRing.{u2} R] [_inst_3 : CommRing.{u1} S] (p : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))), Eq.{max (succ u3) (succ u1)} (Finsupp.{u3, u1} (Finsupp.{u3, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) S (MulZeroOneClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))))) (Finsupp.mapRange.{u3, u2, u1} (Finsupp.{u3, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R S (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (MulZeroOneClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S 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(MvPolynomial.map.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_2) (CommRing.toCommSemiring.{u1} S _inst_3) f) p)
+  forall (σ : Type.{u3}) {R : Type.{u2}} {S : Type.{u1}} [_inst_2 : CommRing.{u2} R] [_inst_3 : CommRing.{u1} S] (p : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))), Eq.{max (succ u3) (succ u1)} (Finsupp.{u3, u1} (Finsupp.{u3, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) S (MulZeroOneClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun 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(CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S 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(MvPolynomial.map.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_2) (CommRing.toCommSemiring.{u1} S _inst_3) f) p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_range_eq_map MvPolynomial.mapRange_eq_mapₓ'. -/
 theorem mapRange_eq_map {R S : Type _} [CommRing R] [CommRing S] (p : MvPolynomial σ R)
     (f : R →+* S) : Finsupp.mapRange f f.map_zero p = map f p :=

2f5b500a

bump to nightly-2023-05-18-03

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

b46e9d53

Diff

@@ -146,7 +146,7 @@ def basisMonomials : Basis (σ →₀ ℕ) R (MvPolynomial σ R) :=
 lean 3 declaration is
   forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommRing.{u2} R], Eq.{max (succ u1) (succ u2)} ((fun (_x : Basis.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) => (Finsupp.{u1, 0} σ Nat Nat.hasZero) -> (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (coeFn.{max (succ u1) (succ u2) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (Basis.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) 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(CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => R -> (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.monomial.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))
 but is expected to have type
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(MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (Basis.funLike.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (fun (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.monomial.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
+  forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommRing.{u2} R], Eq.{max (succ u1) (succ u2)} (forall (a : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (Basis.{u1, u2, max u2 u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (Basis.funLike.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (fun (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.monomial.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_basis_monomials MvPolynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials :
@@ -179,7 +179,7 @@ noncomputable def basisMonomials : Basis ℕ R R[X] :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} ((fun (_x : Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => Nat -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.basisMonomials.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => Nat -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (FunLike.hasCoeToFun.{succ u1, 1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) Nat (fun (_x : Nat) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.funLike.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.basisMonomials.{u1} R _inst_1)) (fun (s : Nat) => coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) s) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (forall (a : Nat), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (FunLike.coe.{succ u1, 1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) Nat (fun (_x : Nat) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (Basis.funLike.{0, u1, u1} Nat R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.basisMonomials.{u1} R _inst_1)) (fun (s : Nat) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) s) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (forall (a : Nat), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (FunLike.coe.{succ u1, 1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) Nat (fun (_x : Nat) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (Basis.funLike.{0, u1, u1} Nat R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.basisMonomials.{u1} R _inst_1)) (fun (s : Nat) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) s) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_basis_monomials Polynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials : (basisMonomials R : ℕ → R[X]) = fun s => monomial s 1 :=

2f5b500a

bump to nightly-2023-05-16-03

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

4c01fe25

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module ring_theory.mv_polynomial.basic
-! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
+! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -44,8 +44,6 @@ Generalise to noncommutative (semi)rings
 
 noncomputable section
 
-open Classical
-
 open Set LinearMap Submodule
 
 open BigOperators Polynomial
@@ -121,15 +119,19 @@ theorem mem_restrictDegree (p : MvPolynomial σ R) (n : ℕ) :
 #align mv_polynomial.mem_restrict_degree MvPolynomial.mem_restrictDegree
 -/
 
-#print MvPolynomial.mem_restrictDegree_iff_sup /-
-theorem mem_restrictDegree_iff_sup (p : MvPolynomial σ R) (n : ℕ) :
+/- warning: mv_polynomial.mem_restrict_degree_iff_sup -> MvPolynomial.mem_restrictDegree_iff_sup is a dubious translation:
+lean 3 declaration is
+  forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] [_inst_2 : DecidableEq.{succ u1} σ] (p : MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (n : Nat), Iff (Membership.Mem.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (SetLike.hasMem.{max u1 u2, max u1 u2} (Submodule.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.setLike.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)))))) p (MvPolynomial.restrictDegree.{u1, u2} σ R _inst_1 n)) (forall (i : σ), LE.le.{0} Nat Nat.hasLe (Multiset.count.{u1} σ (fun (a : σ) (b : σ) => _inst_2 a b) i (MvPolynomial.degrees.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) p)) n)
+but is expected to have type
+  forall (σ : Type.{u1}) {R : Type.{u2}} [_inst_1 : CommRing.{u2} R] (_inst_2 : MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (p : Nat), Iff (Membership.mem.{max u1 u2, max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (SetLike.instMembership.{max u1 u2, max u1 u2} (Submodule.{u2, max u2 u1} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Submodule.setLike.{u2, max u1 u2} R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))))) _inst_2 (MvPolynomial.restrictDegree.{u1, u2} σ R _inst_1 p)) (forall (i : σ), LE.le.{0} Nat instLENat (Multiset.count.{u1} σ (fun (a : σ) (b : σ) => Classical.propDecidable (Eq.{succ u1} σ a b)) i (MvPolynomial.degrees.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) _inst_2)) p)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.mem_restrict_degree_iff_sup MvPolynomial.mem_restrictDegree_iff_supₓ'. -/
+theorem mem_restrictDegree_iff_sup [DecidableEq σ] (p : MvPolynomial σ R) (n : ℕ) :
     p ∈ restrictDegree σ R n ↔ ∀ i, p.degrees.count i ≤ n :=
   by
-  simp only [mem_restrict_degree, degrees, Multiset.count_finset_sup, Finsupp.count_toMultiset,
+  simp only [mem_restrict_degree, degrees_def, Multiset.count_finset_sup, Finsupp.count_toMultiset,
     Finset.sup_le_iff]
   exact ⟨fun h n s hs => h s hs n, fun h s hs n => h n s hs⟩
 #align mv_polynomial.mem_restrict_degree_iff_sup MvPolynomial.mem_restrictDegree_iff_sup
--/
 
 variable (σ R)

19cb3751

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -69,7 +69,7 @@ section Homomorphism
 lean 3 declaration is
   forall (σ : Type.{u1}) {R : Type.{u2}} {S : Type.{u3}} [_inst_2 : CommRing.{u2} R] [_inst_3 : CommRing.{u3} S] (p : MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (f : RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))), Eq.{max (succ u1) (succ u3)} (Finsupp.{u1, u3} (Finsupp.{u1, 0} σ Nat Nat.hasZero) S (MulZeroClass.toHasZero.{u3} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3))))))) (Finsupp.mapRange.{u1, u2, u3} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R S (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))) (MulZeroClass.toHasZero.{u3} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))) (fun (_x : RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))) => R -> S) (RingHom.hasCoeToFun.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))) f) (RingHom.map_zero.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3))) f) p) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (MvPolynomial.commSemiring.{u3, u1} S σ (CommRing.toCommSemiring.{u3} S _inst_3))))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (MvPolynomial.commSemiring.{u3, u1} S σ (CommRing.toCommSemiring.{u3} S _inst_3))))) => (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) -> (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3))) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (MvPolynomial.commSemiring.{u3, u1} S σ (CommRing.toCommSemiring.{u3} S _inst_3))))) (MvPolynomial.map.{u2, u3, u1} R S σ (CommRing.toCommSemiring.{u2} R _inst_2) (CommRing.toCommSemiring.{u3} S _inst_3) f) p)
 but is expected to have type
-  forall (σ : Type.{u3}) {R : Type.{u2}} {S : Type.{u1}} [_inst_2 : CommRing.{u2} R] [_inst_3 : CommRing.{u1} S] (p : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))), Eq.{max (succ u3) (succ u1)} (Finsupp.{u3, u1} (Finsupp.{u3, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) S (MulZeroOneClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))))) (Finsupp.mapRange.{u3, u2, u1} (Finsupp.{u3, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R S (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))))) (MulZeroOneClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))))))) f) (RingHom.map_zero.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))) f) p) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (RingHom.{max u2 u3, max u1 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (MvPolynomial.commSemiring.{u1, u3} S 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(CommRing.toCommSemiring.{u1} S _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_3))))) (RingHomClass.toNonUnitalRingHomClass.{max (max u2 u1) u3, max u2 u3, max u1 u3} (RingHom.{max u2 u3, max u1 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_3))))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_3)))) (RingHom.instRingHomClassRingHom.{max u2 u3, max u1 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_3)))))))) (MvPolynomial.map.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_2) (CommRing.toCommSemiring.{u1} S _inst_3) f) p)
+  forall (σ : Type.{u3}) {R : Type.{u2}} {S : Type.{u1}} [_inst_2 : CommRing.{u2} R] [_inst_3 : CommRing.{u1} S] (p : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (f : RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))), Eq.{max (succ u3) (succ u1)} (Finsupp.{u3, u1} (Finsupp.{u3, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) S (MulZeroOneClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))))) (Finsupp.mapRange.{u3, u2, u1} (Finsupp.{u3, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R S (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (MulZeroOneClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))))))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3)))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))))))) f) (RingHom.map_zero.{u1, u2} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (Semiring.toNonAssocSemiring.{u1} S (CommSemiring.toSemiring.{u1} S (CommRing.toCommSemiring.{u1} S _inst_3))) f) p) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (RingHom.{max u2 u3, max u1 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S 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(MvPolynomial.map.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_2) (CommRing.toCommSemiring.{u1} S _inst_3) f) p)
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_range_eq_map MvPolynomial.mapRange_eq_mapₓ'. -/
 theorem mapRange_eq_map {R S : Type _} [CommRing R] [CommRing S] (p : MvPolynomial σ R)
     (f : R →+* S) : Finsupp.mapRange f f.map_zero p = map f p :=
@@ -144,7 +144,7 @@ def basisMonomials : Basis (σ →₀ ℕ) R (MvPolynomial σ R) :=
 lean 3 declaration is
   forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommRing.{u2} R], Eq.{max (succ u1) (succ u2)} ((fun (_x : Basis.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) => (Finsupp.{u1, 0} σ Nat Nat.hasZero) -> (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (coeFn.{max (succ u1) (succ u2) (succ (max u1 u2)), max (succ u1) (succ (max u1 u2))} (Basis.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (fun (_x : Basis.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) => (Finsupp.{u1, 0} σ Nat Nat.hasZero) -> (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1))) (FunLike.hasCoeToFun.{max (succ u1) (succ u2) (succ (max u1 u2)), succ u1, succ (max u1 u2)} (Basis.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} 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(CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (fun (_x : LinearMap.{u2, u2, u2, max u1 u2} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) => R -> (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1))) (LinearMap.hasCoeToFun.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.monomial.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s) (OfNat.ofNat.{u2} R 1 (OfNat.mk.{u2} R 1 (One.one.{u2} R (AddMonoidWithOne.toOne.{u2} R (AddGroupWithOne.toAddMonoidWithOne.{u2} R (AddCommGroupWithOne.toAddGroupWithOne.{u2} R (Ring.toAddCommGroupWithOne.{u2} R (CommRing.toRing.{u2} R _inst_1)))))))))
 but is expected to have type
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(CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (Basis.funLike.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (fun (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.monomial.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (NonAssocRing.toOne.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1))))))
+  forall (σ : Type.{u1}) (R : Type.{u2}) [_inst_1 : CommRing.{u2} R], Eq.{max (succ u1) (succ u2)} (forall (a : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) a) (FunLike.coe.{max (succ u1) (succ u2), succ u1, max (succ u1) (succ u2)} (Basis.{u1, u2, max u2 u1} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) (fun (_x : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (Basis.funLike.{u1, u2, max u1 u2} (Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (fun (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u2, max u1 u2} R R R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{max u2 u1} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1)))))) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (MvPolynomial.module.{u2, u2, u1} R R σ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommRing.toCommSemiring.{u2} R _inst_1) (Semiring.toModule.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (MvPolynomial.monomial.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_1) s) (OfNat.ofNat.{u2} R 1 (One.toOfNat1.{u2} R (Semiring.toOne.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_basis_monomials MvPolynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials :
@@ -177,7 +177,7 @@ noncomputable def basisMonomials : Basis ℕ R R[X] :=
 lean 3 declaration is
   forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} ((fun (_x : Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => Nat -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.basisMonomials.{u1} R _inst_1)) (coeFn.{succ u1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => Nat -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (FunLike.hasCoeToFun.{succ u1, 1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) Nat (fun (_x : Nat) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Basis.funLike.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toAddCommGroup.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.basisMonomials.{u1} R _inst_1)) (fun (s : Nat) => coeFn.{succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (LinearMap.hasCoeToFun.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) s) (OfNat.ofNat.{u1} R 1 (OfNat.mk.{u1} R 1 (One.one.{u1} R (AddMonoidWithOne.toOne.{u1} R (AddGroupWithOne.toAddMonoidWithOne.{u1} R (AddCommGroupWithOne.toAddGroupWithOne.{u1} R (Ring.toAddCommGroupWithOne.{u1} R (CommRing.toRing.{u1} R _inst_1)))))))))
 but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (forall (a : Nat), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) a) (FunLike.coe.{succ u1, 1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) Nat (fun (_x : Nat) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (Basis.funLike.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.basisMonomials.{u1} R _inst_1)) (fun (s : Nat) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) s) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+  forall (R : Type.{u1}) [_inst_1 : CommRing.{u1} R], Eq.{succ u1} (forall (a : Nat), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) a) (FunLike.coe.{succ u1, 1, succ u1} (Basis.{0, u1, u1} Nat R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) Nat (fun (_x : Nat) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (Basis.funLike.{0, u1, u1} Nat R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Polynomial.monomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) s) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))
 Case conversion may be inaccurate. Consider using '#align polynomial.coe_basis_monomials Polynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials : (basisMonomials R : ℕ → R[X]) = fun s => monomial s 1 :=

19cb3751

bump to nightly-2023-04-09-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

32290448

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module ring_theory.mv_polynomial.basic
-! leanprover-community/mathlib commit 019ead10c09bb91f49b1b7005d442960b1e0485f
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.LinearAlgebra.FinsuppVectorSpace
 /-!
 # Multivariate polynomials over commutative rings
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains basic facts about multivariate polynomials over commutative rings, for example
 that the monomials form a basis.

019ead10

bump to nightly-2023-04-07-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

a23075a3

Diff

@@ -62,6 +62,12 @@ end CharP
 
 section Homomorphism
 
+/- warning: mv_polynomial.map_range_eq_map -> MvPolynomial.mapRange_eq_map is a dubious translation:
+lean 3 declaration is
+  forall (σ : Type.{u1}) {R : Type.{u2}} {S : Type.{u3}} [_inst_2 : CommRing.{u2} R] [_inst_3 : CommRing.{u3} S] (p : MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (f : RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))), Eq.{max (succ u1) (succ u3)} (Finsupp.{u1, u3} (Finsupp.{u1, 0} σ Nat Nat.hasZero) S (MulZeroClass.toHasZero.{u3} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3))))))) (Finsupp.mapRange.{u1, u2, u3} (Finsupp.{u1, 0} σ Nat Nat.hasZero) R S (MulZeroClass.toHasZero.{u2} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))) (MulZeroClass.toHasZero.{u3} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))))) (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))) (fun (_x : RingHom.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))) => R -> S) (RingHom.hasCoeToFun.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3)))) f) (RingHom.map_zero.{u2, u3} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} S (Ring.toNonAssocRing.{u3} S (CommRing.toRing.{u3} S _inst_3))) f) p) (coeFn.{max (succ (max u1 u2)) (succ (max u1 u3)), max (succ (max u1 u2)) (succ (max u1 u3))} (RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (MvPolynomial.commSemiring.{u3, u1} S σ (CommRing.toCommSemiring.{u3} S _inst_3))))) (fun (_x : RingHom.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (MvPolynomial.commSemiring.{u3, u1} S σ (CommRing.toCommSemiring.{u3} S _inst_3))))) => (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) -> (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3))) (RingHom.hasCoeToFun.{max u1 u2, max u1 u3} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u1 u2} (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u1} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} σ S (CommRing.toCommSemiring.{u3} S _inst_3)) (MvPolynomial.commSemiring.{u3, u1} S σ (CommRing.toCommSemiring.{u3} S _inst_3))))) (MvPolynomial.map.{u2, u3, u1} R S σ (CommRing.toCommSemiring.{u2} R _inst_2) (CommRing.toCommSemiring.{u3} S _inst_3) f) p)
+but is expected to have type
+  forall (σ : Type.{u3}) {R : Type.{u2}} {S : Type.{u1}} [_inst_2 : CommRing.{u2} R] [_inst_3 : CommRing.{u1} S] (p : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (f : RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))), Eq.{max (succ u3) (succ u1)} (Finsupp.{u3, u1} (Finsupp.{u3, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) S (MulZeroOneClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))))) (Finsupp.mapRange.{u3, u2, u1} (Finsupp.{u3, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) R S (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))))) (MulZeroOneClass.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))))) (NonAssocSemiring.toMulZeroOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (MulZeroOneClass.toZero.{u2} R (NonAssocSemiring.toMulZeroOneClass.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2)))))))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} S (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3)))) R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))) (RingHom.instRingHomClassRingHom.{u2, u1} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))))))) f) (RingHom.map_zero.{u1, u2} R S (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_2))) (NonAssocRing.toNonAssocSemiring.{u1} S (Ring.toNonAssocRing.{u1} S (CommRing.toRing.{u1} S _inst_3))) f) p) (FunLike.coe.{max (max (succ u2) (succ u1)) (succ u3), max (succ u2) (succ u3), max (succ u1) (succ u3)} (RingHom.{max u2 u3, max u1 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_3))))) (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (_x : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) => MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) _x) (MulHomClass.toFunLike.{max (max u2 u1) u3, max u2 u3, max u1 u3} (RingHom.{max u2 u3, max u1 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S 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(MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (Semiring.toNonAssocSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{max u2 u3} (MvPolynomial.{u3, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_2)) (MvPolynomial.commSemiring.{u2, u3} R σ (CommRing.toCommSemiring.{u2} R _inst_2)))) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} σ S (CommRing.toCommSemiring.{u1} S _inst_3)) (MvPolynomial.commSemiring.{u1, u3} S σ (CommRing.toCommSemiring.{u1} S _inst_3)))))))) (MvPolynomial.map.{u2, u1, u3} R S σ (CommRing.toCommSemiring.{u2} R _inst_2) (CommRing.toCommSemiring.{u1} S _inst_3) f) p)
+Case conversion may be inaccurate. Consider using '#align mv_polynomial.map_range_eq_map MvPolynomial.mapRange_eq_mapₓ'. -/
 theorem mapRange_eq_map {R S : Type _} [CommRing R] [CommRing S] (p : MvPolynomial σ R)
     (f : R →+* S) : Finsupp.mapRange f f.map_zero p = map f p :=
   by
@@ -77,33 +83,42 @@ end Homomorphism
 
 section Degree
 
+#print MvPolynomial.restrictTotalDegree /-
 /-- The submodule of polynomials of total degree less than or equal to `m`.-/
 def restrictTotalDegree : Submodule R (MvPolynomial σ R) :=
   Finsupp.supported _ _ { n | (n.Sum fun n e => e) ≤ m }
 #align mv_polynomial.restrict_total_degree MvPolynomial.restrictTotalDegree
+-/
 
+#print MvPolynomial.restrictDegree /-
 /-- The submodule of polynomials such that the degree with respect to each individual variable is
 less than or equal to `m`.-/
 def restrictDegree (m : ℕ) : Submodule R (MvPolynomial σ R) :=
   Finsupp.supported _ _ { n | ∀ i, n i ≤ m }
 #align mv_polynomial.restrict_degree MvPolynomial.restrictDegree
+-/
 
 variable {R}
 
+#print MvPolynomial.mem_restrictTotalDegree /-
 theorem mem_restrictTotalDegree (p : MvPolynomial σ R) :
     p ∈ restrictTotalDegree σ R m ↔ p.totalDegree ≤ m :=
   by
   rw [total_degree, Finset.sup_le_iff]
   rfl
 #align mv_polynomial.mem_restrict_total_degree MvPolynomial.mem_restrictTotalDegree
+-/
 
+#print MvPolynomial.mem_restrictDegree /-
 theorem mem_restrictDegree (p : MvPolynomial σ R) (n : ℕ) :
     p ∈ restrictDegree σ R n ↔ ∀ s ∈ p.support, ∀ i, (s : σ →₀ ℕ) i ≤ n :=
   by
   rw [restrict_degree, Finsupp.mem_supported]
   rfl
 #align mv_polynomial.mem_restrict_degree MvPolynomial.mem_restrictDegree
+-/
 
+#print MvPolynomial.mem_restrictDegree_iff_sup /-
 theorem mem_restrictDegree_iff_sup (p : MvPolynomial σ R) (n : ℕ) :
     p ∈ restrictDegree σ R n ↔ ∀ i, p.degrees.count i ≤ n :=
   by
@@ -111,24 +126,35 @@ theorem mem_restrictDegree_iff_sup (p : MvPolynomial σ R) (n : ℕ) :
     Finset.sup_le_iff]
   exact ⟨fun h n s hs => h s hs n, fun h s hs n => h n s hs⟩
 #align mv_polynomial.mem_restrict_degree_iff_sup MvPolynomial.mem_restrictDegree_iff_sup
+-/
 
 variable (σ R)
 
+#print MvPolynomial.basisMonomials /-
 /-- The monomials form a basis on `mv_polynomial σ R`. -/
 def basisMonomials : Basis (σ →₀ ℕ) R (MvPolynomial σ R) :=
   Finsupp.basisSingleOne
 #align mv_polynomial.basis_monomials MvPolynomial.basisMonomials
+-/
 
+/- warning: mv_polynomial.coe_basis_monomials -> MvPolynomial.coe_basisMonomials is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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R _inst_1) (Semiring.toModule.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_1))))) (MvPolynomial.basisMonomials.{u1, u2} σ R _inst_1)) (fun (s : Finsupp.{u1, 0} σ Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero)) => FunLike.coe.{max (succ u1) (succ u2), succ u2, max (succ u1) (succ u2)} (LinearMap.{u2, u2, u2, max u2 u1} R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) R (MvPolynomial.{u1, u2} σ R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u2 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+Case conversion may be inaccurate. Consider using '#align mv_polynomial.coe_basis_monomials MvPolynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials :
     (basisMonomials σ R : (σ →₀ ℕ) → MvPolynomial σ R) = fun s => monomial s 1 :=
   rfl
 #align mv_polynomial.coe_basis_monomials MvPolynomial.coe_basisMonomials
 
-theorem linearIndependent_x : LinearIndependent R (X : σ → MvPolynomial σ R) :=
+#print MvPolynomial.linearIndependent_X /-
+theorem linearIndependent_X : LinearIndependent R (X : σ → MvPolynomial σ R) :=
   (basisMonomials σ R).LinearIndependent.comp (fun s : σ => Finsupp.single s 1)
     (Finsupp.single_left_injective one_ne_zero)
-#align mv_polynomial.linear_independent_X MvPolynomial.linearIndependent_x
+#align mv_polynomial.linear_independent_X MvPolynomial.linearIndependent_X
+-/
 
 end Degree
 
@@ -137,11 +163,19 @@ end MvPolynomial
 -- this is here to avoid import cycle issues
 namespace Polynomial
 
+#print Polynomial.basisMonomials /-
 /-- The monomials form a basis on `R[X]`. -/
 noncomputable def basisMonomials : Basis ℕ R R[X] :=
   Basis.ofRepr (toFinsuppIsoAlg R).toLinearEquiv
 #align polynomial.basis_monomials Polynomial.basisMonomials
+-/
 
+/- warning: polynomial.coe_basis_monomials -> Polynomial.coe_basisMonomials is a dubious translation:
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(Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) Nat (fun (_x : Nat) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Nat) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (Basis.funLike.{0, u1, u1} Nat R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocRing.toNonUnitalNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toNonAssocRing.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.ring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.basisMonomials.{u1} R _inst_1)) (fun (s : Nat) => FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u1, u1, u1, u1} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : R) => Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u1, u1} R R R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))))) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.module.{u1, u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.monomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) s) (OfNat.ofNat.{u1} R 1 (One.toOfNat1.{u1} R (NonAssocRing.toOne.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.coe_basis_monomials Polynomial.coe_basisMonomialsₓ'. -/
 @[simp]
 theorem coe_basisMonomials : (basisMonomials R : ℕ → R[X]) = fun s => monomial s 1 :=
   funext fun n => ofFinsupp_single _ _

019ead10

bump to nightly-2023-03-23-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

53b827ba

Diff

@@ -139,7 +139,7 @@ namespace Polynomial
 
 /-- The monomials form a basis on `R[X]`. -/
 noncomputable def basisMonomials : Basis ℕ R R[X] :=
-  Basis.of_repr (toFinsuppIsoAlg R).toLinearEquiv
+  Basis.ofRepr (toFinsuppIsoAlg R).toLinearEquiv
 #align polynomial.basis_monomials Polynomial.basisMonomials
 
 @[simp]

019ead10

bump to nightly-2023-03-15-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

f73428b0

Diff

@@ -125,7 +125,7 @@ theorem coe_basisMonomials :
   rfl
 #align mv_polynomial.coe_basis_monomials MvPolynomial.coe_basisMonomials
 
-theorem linearIndependent_x : LinearIndependent R (x : σ → MvPolynomial σ R) :=
+theorem linearIndependent_x : LinearIndependent R (X : σ → MvPolynomial σ R) :=
   (basisMonomials σ R).LinearIndependent.comp (fun s : σ => Finsupp.single s 1)
     (Finsupp.single_left_injective one_ne_zero)
 #align mv_polynomial.linear_independent_X MvPolynomial.linearIndependent_x

019ead10

bump to nightly-2023-03-08-10

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

422cc012

Diff

@@ -144,7 +144,7 @@ noncomputable def basisMonomials : Basis ℕ R R[X] :=
 
 @[simp]
 theorem coe_basisMonomials : (basisMonomials R : ℕ → R[X]) = fun s => monomial s 1 :=
-  funext fun n => of_finsupp_single _ _
+  funext fun n => ofFinsupp_single _ _
 #align polynomial.coe_basis_monomials Polynomial.coe_basisMonomials
 
 end Polynomial

019ead10

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

2f5b500a

feat(RingTheory/MvPolynomial): freeness of MvPolynomial (#12392)

Shows that a multivariable polynomial ring is a free module.

c0fb6482

Diff

@@ -141,6 +141,10 @@ theorem coe_basisMonomials :
   rfl
 #align mv_polynomial.coe_basis_monomials MvPolynomial.coe_basisMonomials
 
+/-- The `R`-module `MvPolynomial σ R` is free. -/
+instance : Module.Free R (MvPolynomial σ R) :=
+  Module.Free.of_basis (MvPolynomial.basisMonomials σ R)
+
 theorem linearIndependent_X : LinearIndependent R (X : σ → MvPolynomial σ R) :=
   (basisMonomials σ R).linearIndependent.comp (fun s : σ => Finsupp.single s 1)
     (Finsupp.single_left_injective one_ne_zero)

2f5b500a

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -91,13 +91,13 @@ theorem restrictSupport_mono {s t : Set (σ →₀ ℕ)} (h : s ⊆ t) :
 
 variable (σ)
 
-/-- The submodule of polynomials of total degree less than or equal to `m`.-/
+/-- The submodule of polynomials of total degree less than or equal to `m`. -/
 def restrictTotalDegree (m : ℕ) : Submodule R (MvPolynomial σ R) :=
   restrictSupport R { n | (n.sum fun _ e => e) ≤ m }
 #align mv_polynomial.restrict_total_degree MvPolynomial.restrictTotalDegree
 
 /-- The submodule of polynomials such that the degree with respect to each individual variable is
-less than or equal to `m`.-/
+less than or equal to `m`. -/
 def restrictDegree (m : ℕ) : Submodule R (MvPolynomial σ R) :=
   restrictSupport R { n | ∀ i, n i ≤ m }
 #align mv_polynomial.restrict_degree MvPolynomial.restrictDegree

2f5b500a

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

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

56e439ec

Diff

@@ -4,8 +4,8 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
 import Mathlib.Algebra.CharP.Basic
-import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.MvPolynomial.Degrees
+import Mathlib.Algebra.MvPolynomial.Degrees
+import Mathlib.Algebra.Polynomial.AlgebraMap
 import Mathlib.LinearAlgebra.FinsuppVectorSpace
 import Mathlib.LinearAlgebra.FreeModule.Finite.Basic

2f5b500a

chore(*): migrate from RingHom.map_* to _root_.map_* (#11660)

Cherry-picked from #9607 Co-authored-by: @semorrison

859f3760

Diff

@@ -67,7 +67,7 @@ section Homomorphism
 
 theorem mapRange_eq_map {R S : Type*} [CommSemiring R] [CommSemiring S] (p : MvPolynomial σ R)
     (f : R →+* S) : Finsupp.mapRange f f.map_zero p = map f p := by
-  rw [p.as_sum, Finsupp.mapRange_finset_sum, (map f).map_sum]
+  rw [p.as_sum, Finsupp.mapRange_finset_sum, map_sum (map f)]
   refine' Finset.sum_congr rfl fun n _ => _
   rw [map_monomial, ← single_eq_monomial, Finsupp.mapRange_single, single_eq_monomial]
 #align mv_polynomial.map_range_eq_map MvPolynomial.mapRange_eq_map

2f5b500a

chore: split MvPolynomial.Variables (#11094)

Splits this file into two. The sections about degree related concepts are totally independent of the vars related concepts so this was a clean split.

7f32cc79

Diff

@@ -5,7 +5,7 @@ Authors: Johannes Hölzl
 -/
 import Mathlib.Algebra.CharP.Basic
 import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.MvPolynomial.Variables
+import Mathlib.Data.MvPolynomial.Degrees
 import Mathlib.LinearAlgebra.FinsuppVectorSpace
 import Mathlib.LinearAlgebra.FreeModule.Finite.Basic

2f5b500a

chore: golf #10193 (#10205)

add rename_isHomogeneous without Injective assumption, and rename rename_isHomogeneous to rename_isHomogeneous_iff.
refactor degreeOf_le_totalDegree through restrictTotalDegree_le_restrictDegree

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

1a8eb3bd

Diff

@@ -102,12 +102,6 @@ def restrictDegree (m : ℕ) : Submodule R (MvPolynomial σ R) :=
   restrictSupport R { n | ∀ i, n i ≤ m }
 #align mv_polynomial.restrict_degree MvPolynomial.restrictDegree
 
-theorem restrictTotalDegree_le_restrictDegree (m : ℕ) :
-    restrictTotalDegree σ R m ≤ restrictDegree σ R m :=
-  restrictSupport_mono R fun n hn i ↦ (eq_or_ne (n i) 0).elim
-    (fun h ↦ h.trans_le m.zero_le) fun h ↦
-      (Finset.single_le_sum (fun _ _ ↦ Nat.zero_le _) <| Finsupp.mem_support_iff.mpr h).trans hn
-
 variable {R}
 
 theorem mem_restrictTotalDegree (p : MvPolynomial σ R) :
@@ -131,6 +125,11 @@ theorem mem_restrictDegree_iff_sup [DecidableEq σ] (p : MvPolynomial σ R) (n :
 
 variable (R)
 
+theorem restrictTotalDegree_le_restrictDegree (m : ℕ) :
+    restrictTotalDegree σ R m ≤ restrictDegree σ R m :=
+  fun p hp ↦ (mem_restrictDegree _ _ _).mpr fun s hs i ↦ (degreeOf_le_iff.mp
+    (degreeOf_le_totalDegree p i) s hs).trans ((mem_restrictTotalDegree _ _ _).mp hp)
+
 /-- The monomials form a basis on `MvPolynomial σ R`. -/
 def basisMonomials : Basis (σ →₀ ℕ) R (MvPolynomial σ R) :=
   Finsupp.basisSingleOne

2f5b500a

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -5,7 +5,6 @@ Authors: Johannes Hölzl
 -/
 import Mathlib.Algebra.CharP.Basic
 import Mathlib.Data.Polynomial.AlgebraMap
-import Mathlib.Data.MvPolynomial.CommRing
 import Mathlib.Data.MvPolynomial.Variables
 import Mathlib.LinearAlgebra.FinsuppVectorSpace
 import Mathlib.LinearAlgebra.FreeModule.Finite.Basic

2f5b500a

chore(*): rename FunLike to DFunLike (#9785)

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

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

82656743

Diff

@@ -151,7 +151,7 @@ set_option linter.uppercaseLean3 false in
 
 private lemma finite_setOf_bounded (α) [Finite α] (n : ℕ) : Finite {f : α →₀ ℕ | ∀ a, f a ≤ n} :=
   ((Set.Finite.pi' fun _ ↦ Set.finite_le_nat _).preimage <|
-    FunLike.coe_injective.injOn _).to_subtype
+    DFunLike.coe_injective.injOn _).to_subtype
 
 instance [Finite σ] (N : ℕ) : Module.Finite R (restrictDegree σ R N) :=
   have := finite_setOf_bounded σ N

2f5b500a

chore(*): replace $ with <| (#9319)

See Zulip thread for the discussion.

9f6d3388

Diff

@@ -150,7 +150,8 @@ set_option linter.uppercaseLean3 false in
 #align mv_polynomial.linear_independent_X MvPolynomial.linearIndependent_X
 
 private lemma finite_setOf_bounded (α) [Finite α] (n : ℕ) : Finite {f : α →₀ ℕ | ∀ a, f a ≤ n} :=
-  ((Set.Finite.pi' fun _ ↦ Set.finite_le_nat _).preimage $ FunLike.coe_injective.injOn _).to_subtype
+  ((Set.Finite.pi' fun _ ↦ Set.finite_le_nat _).preimage <|
+    FunLike.coe_injective.injOn _).to_subtype
 
 instance [Finite σ] (N : ℕ) : Module.Finite R (restrictDegree σ R N) :=
   have := finite_setOf_bounded σ N

2f5b500a

chore: move a few results from Archive.Hairer into mathlib (#9315)

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

87ffb361

Diff

@@ -8,6 +8,7 @@ import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.Data.MvPolynomial.CommRing
 import Mathlib.Data.MvPolynomial.Variables
 import Mathlib.LinearAlgebra.FinsuppVectorSpace
+import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
 
 #align_import ring_theory.mv_polynomial.basic from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
 
@@ -148,6 +149,22 @@ theorem linearIndependent_X : LinearIndependent R (X : σ → MvPolynomial σ R)
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.linear_independent_X MvPolynomial.linearIndependent_X
 
+private lemma finite_setOf_bounded (α) [Finite α] (n : ℕ) : Finite {f : α →₀ ℕ | ∀ a, f a ≤ n} :=
+  ((Set.Finite.pi' fun _ ↦ Set.finite_le_nat _).preimage $ FunLike.coe_injective.injOn _).to_subtype
+
+instance [Finite σ] (N : ℕ) : Module.Finite R (restrictDegree σ R N) :=
+  have := finite_setOf_bounded σ N
+  Module.Finite.of_basis (basisRestrictSupport R _)
+
+instance [Finite σ] (N : ℕ) : Module.Finite R (restrictTotalDegree σ R N) :=
+  have := finite_setOf_bounded σ N
+  have : Finite {s : σ →₀ ℕ | s.sum (fun _ e ↦ e) ≤ N} := by
+    rw [Set.finite_coe_iff] at this ⊢
+    exact this.subset fun n hn i ↦ (eq_or_ne (n i) 0).elim
+      (fun h ↦ h.trans_le N.zero_le) fun h ↦
+        (Finset.single_le_sum (fun _ _ ↦ Nat.zero_le _) <| Finsupp.mem_support_iff.mpr h).trans hn
+  Module.Finite.of_basis (basisRestrictSupport R _)
+
 end Degree
 
 end MvPolynomial

2f5b500a

archive: smooth functions whose integral calculates the values of polynomials (#9138)

Test case of the library suggested by Martin Hairer, see https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Hairer.20challenge/near/404836147.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net>

98e2ce28

Diff

@@ -76,17 +76,38 @@ end Homomorphism
 
 section Degree
 
+variable {σ}
+
+/-- The submodule of polynomials that are sum of monomials in the set `s`. -/
+def restrictSupport (s : Set (σ →₀ ℕ)) : Submodule R (MvPolynomial σ R) :=
+  Finsupp.supported _ _ s
+
+/-- `restrictSupport R s` has a canonical `R`-basis indexed by `s`. -/
+def basisRestrictSupport (s : Set (σ →₀ ℕ)) : Basis s R (restrictSupport R s) where
+  repr := Finsupp.supportedEquivFinsupp s
+
+theorem restrictSupport_mono {s t : Set (σ →₀ ℕ)} (h : s ⊆ t) :
+    restrictSupport R s ≤ restrictSupport R t := Finsupp.supported_mono h
+
+variable (σ)
+
 /-- The submodule of polynomials of total degree less than or equal to `m`.-/
-def restrictTotalDegree : Submodule R (MvPolynomial σ R) :=
-  Finsupp.supported _ _ { n | (n.sum fun _ e => e) ≤ m }
+def restrictTotalDegree (m : ℕ) : Submodule R (MvPolynomial σ R) :=
+  restrictSupport R { n | (n.sum fun _ e => e) ≤ m }
 #align mv_polynomial.restrict_total_degree MvPolynomial.restrictTotalDegree
 
 /-- The submodule of polynomials such that the degree with respect to each individual variable is
 less than or equal to `m`.-/
 def restrictDegree (m : ℕ) : Submodule R (MvPolynomial σ R) :=
-  Finsupp.supported _ _ { n | ∀ i, n i ≤ m }
+  restrictSupport R { n | ∀ i, n i ≤ m }
 #align mv_polynomial.restrict_degree MvPolynomial.restrictDegree
 
+theorem restrictTotalDegree_le_restrictDegree (m : ℕ) :
+    restrictTotalDegree σ R m ≤ restrictDegree σ R m :=
+  restrictSupport_mono R fun n hn i ↦ (eq_or_ne (n i) 0).elim
+    (fun h ↦ h.trans_le m.zero_le) fun h ↦
+      (Finset.single_le_sum (fun _ _ ↦ Nat.zero_le _) <| Finsupp.mem_support_iff.mpr h).trans hn
+
 variable {R}
 
 theorem mem_restrictTotalDegree (p : MvPolynomial σ R) :
@@ -97,7 +118,7 @@ theorem mem_restrictTotalDegree (p : MvPolynomial σ R) :
 
 theorem mem_restrictDegree (p : MvPolynomial σ R) (n : ℕ) :
     p ∈ restrictDegree σ R n ↔ ∀ s ∈ p.support, ∀ i, (s : σ →₀ ℕ) i ≤ n := by
-  rw [restrictDegree, Finsupp.mem_supported]
+  rw [restrictDegree, restrictSupport, Finsupp.mem_supported]
   rfl
 #align mv_polynomial.mem_restrict_degree MvPolynomial.mem_restrictDegree

2f5b500a

chore: small generalization of finsupp lemmas (#6700)

Noticed whilst doing my other PR about char_zero. Leaves statements that create data alone.

134b6cb8

Diff

@@ -67,12 +67,9 @@ section Homomorphism
 
 theorem mapRange_eq_map {R S : Type*} [CommSemiring R] [CommSemiring S] (p : MvPolynomial σ R)
     (f : R →+* S) : Finsupp.mapRange f f.map_zero p = map f p := by
-  -- `Finsupp.mapRange_finset_sum` expects `f : R →+ S`
-  change Finsupp.mapRange (f : R →+ S) (f : R →+ S).map_zero p = map f p
   rw [p.as_sum, Finsupp.mapRange_finset_sum, (map f).map_sum]
   refine' Finset.sum_congr rfl fun n _ => _
   rw [map_monomial, ← single_eq_monomial, Finsupp.mapRange_single, single_eq_monomial]
-  simp_all only [AddMonoidHom.coe_coe]
 #align mv_polynomial.map_range_eq_map MvPolynomial.mapRange_eq_map
 
 end Homomorphism

2f5b500a

feat: char p for mv_polys over semirings (#6697)

This generalises existing instances to apply to CommSemirings. It also generalises a whole file that was using unnecessarily strong assumptions.

2b6f0012

Diff

@@ -26,8 +26,8 @@ that the monomials form a basis.
 
 ## Main statements
 
-* The multivariate polynomial ring over a commutative ring of positive characteristic has positive
-  characteristic.
+* The multivariate polynomial ring over a commutative semiring of characteristic `p` has
+  characteristic `p`, and similarly for `CharZero`.
 * `basisMonomials`: shows that the monomials form a basis of the vector space of multivariate
   polynomials.
 
@@ -45,7 +45,7 @@ open BigOperators Polynomial
 
 universe u v
 
-variable (σ : Type u) (R : Type v) [CommRing R] (p m : ℕ)
+variable (σ : Type u) (R : Type v) [CommSemiring R] (p m : ℕ)
 
 namespace MvPolynomial
 
@@ -58,13 +58,14 @@ end CharP
 
 section CharZero
 
-instance [CharZero R] : CharZero (MvPolynomial σ R) := CharP.charP_to_charZero (MvPolynomial σ R)
+instance [CharZero R] : CharZero (MvPolynomial σ R) where
+  cast_injective x y hxy := by rwa [← C_eq_coe_nat, ← C_eq_coe_nat, C_inj, Nat.cast_inj] at hxy
 
 end CharZero
 
 section Homomorphism
 
-theorem mapRange_eq_map {R S : Type*} [CommRing R] [CommRing S] (p : MvPolynomial σ R)
+theorem mapRange_eq_map {R S : Type*} [CommSemiring R] [CommSemiring S] (p : MvPolynomial σ R)
     (f : R →+* S) : Finsupp.mapRange f f.map_zero p = map f p := by
   -- `Finsupp.mapRange_finset_sum` expects `f : R →+ S`
   change Finsupp.mapRange (f : R →+ S) (f : R →+ S).map_zero p = map f p

2f5b500a

feat(RingTheory/MvPolynomial/NewtonIdentities): Add proof of Newton's identities (#6139)

Co-authored-by: michaellee94 <michael.a.rodrigues.lee@gmail.com> Co-authored-by: Oliver Nash <github@olivernash.org>

63ae2f41

Diff

@@ -5,6 +5,7 @@ Authors: Johannes Hölzl
 -/
 import Mathlib.Algebra.CharP.Basic
 import Mathlib.Data.Polynomial.AlgebraMap
+import Mathlib.Data.MvPolynomial.CommRing
 import Mathlib.Data.MvPolynomial.Variables
 import Mathlib.LinearAlgebra.FinsuppVectorSpace
 
@@ -55,6 +56,12 @@ instance [CharP R p] : CharP (MvPolynomial σ R) p where
 
 end CharP
 
+section CharZero
+
+instance [CharZero R] : CharZero (MvPolynomial σ R) := CharP.charP_to_charZero (MvPolynomial σ R)
+
+end CharZero
+
 section Homomorphism
 
 theorem mapRange_eq_map {R S : Type*} [CommRing R] [CommRing S] (p : MvPolynomial σ R)

2f5b500a

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

@@ -57,7 +57,7 @@ end CharP
 
 section Homomorphism
 
-theorem mapRange_eq_map {R S : Type _} [CommRing R] [CommRing S] (p : MvPolynomial σ R)
+theorem mapRange_eq_map {R S : Type*} [CommRing R] [CommRing S] (p : MvPolynomial σ R)
     (f : R →+* S) : Finsupp.mapRange f f.map_zero p = map f p := by
   -- `Finsupp.mapRange_finset_sum` expects `f : R →+ S`
   change Finsupp.mapRange (f : R →+ S) (f : R →+ S).map_zero p = map f p

2f5b500a

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) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module ring_theory.mv_polynomial.basic
-! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.CharP.Basic
 import Mathlib.Data.Polynomial.AlgebraMap
 import Mathlib.Data.MvPolynomial.Variables
 import Mathlib.LinearAlgebra.FinsuppVectorSpace
 
+#align_import ring_theory.mv_polynomial.basic from "leanprover-community/mathlib"@"2f5b500a507264de86d666a5f87ddb976e2d8de4"
+
 /-!
 # Multivariate polynomials over commutative rings

2f5b500a

chore: forward-port leanprover-community/mathlib#18848 (#4007)

I've been someone sloppy about forward-porting the exact mathport here; a lot of the classical additions result in the whole proof being indented, which IMO just adds noise to the diff.

What's important is that:

open Classical is removed from all the same files
[DecidableEq _] is added in the same position to all the same lemmas. In theory mathport will detect if we mess this up, so it's not essential to catch this in review. The linter will tell us if it is added unnecessarily, and the build will fail if is not added someewhere it is needed; so only the argument order is at risk of being wrong.
The new foo_def lemmas are all added in variables.lean

7b2fc8ad

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module ring_theory.mv_polynomial.basic
-! leanprover-community/mathlib commit 019ead10c09bb91f49b1b7005d442960b1e0485f
+! leanprover-community/mathlib commit 2f5b500a507264de86d666a5f87ddb976e2d8de4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -41,8 +41,6 @@ Generalise to noncommutative (semi)rings
 
 noncomputable section
 
-open Classical
-
 open Set LinearMap Submodule
 
 open BigOperators Polynomial
@@ -101,9 +99,9 @@ theorem mem_restrictDegree (p : MvPolynomial σ R) (n : ℕ) :
   rfl
 #align mv_polynomial.mem_restrict_degree MvPolynomial.mem_restrictDegree
 
-theorem mem_restrictDegree_iff_sup (p : MvPolynomial σ R) (n : ℕ) :
+theorem mem_restrictDegree_iff_sup [DecidableEq σ] (p : MvPolynomial σ R) (n : ℕ) :
     p ∈ restrictDegree σ R n ↔ ∀ i, p.degrees.count i ≤ n := by
-  simp only [mem_restrictDegree, degrees, Multiset.count_finset_sup, Finsupp.count_toMultiset,
+  simp only [mem_restrictDegree, degrees_def, Multiset.count_finset_sup, Finsupp.count_toMultiset,
     Finset.sup_le_iff]
   exact ⟨fun h n s hs => h s hs n, fun h s hs n => h n s hs⟩
 #align mv_polynomial.mem_restrict_degree_iff_sup MvPolynomial.mem_restrictDegree_iff_sup

019ead10

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

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

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

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

a6e1045f

Diff

@@ -76,13 +76,11 @@ end Homomorphism
 
 section Degree
 
-set_option synthInstance.etaExperiment true in
 /-- The submodule of polynomials of total degree less than or equal to `m`.-/
 def restrictTotalDegree : Submodule R (MvPolynomial σ R) :=
   Finsupp.supported _ _ { n | (n.sum fun _ e => e) ≤ m }
 #align mv_polynomial.restrict_total_degree MvPolynomial.restrictTotalDegree
 
-set_option synthInstance.etaExperiment true in
 /-- The submodule of polynomials such that the degree with respect to each individual variable is
 less than or equal to `m`.-/
 def restrictDegree (m : ℕ) : Submodule R (MvPolynomial σ R) :=
@@ -97,7 +95,6 @@ theorem mem_restrictTotalDegree (p : MvPolynomial σ R) :
   rfl
 #align mv_polynomial.mem_restrict_total_degree MvPolynomial.mem_restrictTotalDegree
 
-set_option synthInstance.etaExperiment true in
 theorem mem_restrictDegree (p : MvPolynomial σ R) (n : ℕ) :
     p ∈ restrictDegree σ R n ↔ ∀ s ∈ p.support, ∀ i, (s : σ →₀ ℕ) i ≤ n := by
   rw [restrictDegree, Finsupp.mem_supported]

019ead10

chore: use etaExperiment rather than hacking with instances (#3668)

This is to fix timeouts in https://github.com/leanprover-community/mathlib4/pull/3552.

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.233552.20.28LinearAlgebra.2EMatrix.2EToLin.29.

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

0f225a7f

Diff

@@ -76,11 +76,13 @@ end Homomorphism
 
 section Degree
 
+set_option synthInstance.etaExperiment true in
 /-- The submodule of polynomials of total degree less than or equal to `m`.-/
 def restrictTotalDegree : Submodule R (MvPolynomial σ R) :=
   Finsupp.supported _ _ { n | (n.sum fun _ e => e) ≤ m }
 #align mv_polynomial.restrict_total_degree MvPolynomial.restrictTotalDegree
 
+set_option synthInstance.etaExperiment true in
 /-- The submodule of polynomials such that the degree with respect to each individual variable is
 less than or equal to `m`.-/
 def restrictDegree (m : ℕ) : Submodule R (MvPolynomial σ R) :=
@@ -95,6 +97,7 @@ theorem mem_restrictTotalDegree (p : MvPolynomial σ R) :
   rfl
 #align mv_polynomial.mem_restrict_total_degree MvPolynomial.mem_restrictTotalDegree
 
+set_option synthInstance.etaExperiment true in
 theorem mem_restrictDegree (p : MvPolynomial σ R) (n : ℕ) :
     p ∈ restrictDegree σ R n ↔ ∀ s ∈ p.support, ∀ i, (s : σ →₀ ℕ) i ≤ n := by
   rw [restrictDegree, Finsupp.mem_supported]

019ead10

feat: port RingTheory.MvPolynomial.Basic (#3329)

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

5a04e704

`ring_theory.mv_polynomial.basic` ⟷ `Mathlib.RingTheory.MvPolynomial.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 512

ring_theory.mv_polynomial.basic ⟷ Mathlib.RingTheory.MvPolynomial.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 512

`ring_theory.mv_polynomial.basic` ⟷ `Mathlib.RingTheory.MvPolynomial.Basic`