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chore(Algebra/Polynomial/Module): workaround for backward.inferInstanceAs #39011

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chore(Algebra/Polynomial/Module): workaround for backward.inferInstanceAs #39011

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13 changes: 8 additions & 5 deletions Mathlib/Algebra/Polynomial/Module/Basic.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -42,14 +42,17 @@ for the full discussion.
def PolynomialModule (R M : Type*) [CommRing R] [AddCommGroup M] [Module R M] := ℕ →₀ M
deriving Inhabited, FunLike, AddCommGroup

set_option backward.inferInstanceAs.wrap.data false in
deriving instance CoeFun for PolynomialModule

variable (R : Type*) {M : Type*} [CommRing R] [AddCommGroup M] [Module R M] (I : Ideal R)
variable {S : Type*} [CommSemiring S] [Algebra S R] [Module S M] [IsScalarTower S R M]

namespace PolynomialModule

/-- Workaround to defeq problems: if we interpret a `PolynomialModule` as a `Finsupp`, also transfer
the `DFunLike` instance. -/
@[simp]
theorem funLike_eq (x : PolynomialModule R M) :
DFunLike.coe (self := Finsupp.instFunLike) x = x := rfl

/-- This is required to have the `IsScalarTower S R M` instance to avoid diamonds. -/
instance : Module S (PolynomialModule R M) :=
inferInstanceAs <| Module S (ℕ →₀ M)
Expand Down Expand Up @@ -174,8 +177,8 @@ def equivPolynomialSelf : PolynomialModule R R ≃ₗ[R[X]] R[X] :=
| add _ _ hp hq => rw [smul_add, map_add, map_add, mul_add, hp, hq]
| single n a =>
ext i
simp_rw [toFinsuppIso_symm_apply, coeff_ofFinsupp, coeff_mul, smul_single_apply,
smul_eq_mul, coeff_ofFinsupp, single_apply, mul_ite, mul_zero]
simp_rw [toFinsuppIso_symm_apply, coeff_ofFinsupp, coeff_mul, funLike_eq, smul_single_apply,
smul_eq_mul, coeff_ofFinsupp, funLike_eq, single_apply, mul_ite, mul_zero]
split_ifs with hn
· rw [Finset.sum_eq_single (i - n, n)]
· simp only [ite_true]
Expand Down
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