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refactor(LinearAlgeba/BilinearMap): Weaken CommSemiring to SMulCommClass #7538

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refactor(LinearAlgeba/BilinearMap): Weaken CommSemiring to SMulCommClass #7538

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f6a70e1
Weaken hypothesis
mans0954 Oct 5, 2023
e069e48
Don't need extra import
mans0954 Oct 6, 2023
5e4ad04
Don't need SMulCommClass condition on R₂
mans0954 Oct 6, 2023
c3d358e
Merge branch 'master' into mans0954/Bilinear-SMulCommClass
mans0954 Oct 6, 2023
eae5824
Better lsmul
mans0954 Oct 6, 2023
05a2cf5
Merge branch 'master' into mans0954/Bilinear-SMulCommClass
mans0954 Oct 6, 2023
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15 changes: 10 additions & 5 deletions Mathlib/LinearAlgebra/BilinearMap.lean
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Expand Up @@ -205,11 +205,11 @@ theorem domRestrict₁₂_apply (f : M →ₛₗ[ρ₁₂] N →ₛₗ[σ₁₂]

end Semiring

section CommSemiring
section SMulCommSemiring

variable {R : Type*} [CommSemiring R] {R₂ : Type*} [CommSemiring R₂]
variable {R : Type*} [Semiring R] {R₂ : Type*} [Semiring R₂]

variable {R₃ : Type*} [CommSemiring R₃] {R₄ : Type*} [CommSemiring R₄]
variable {R₃ : Type*} [Semiring R₃] {R₄ : Type*} [Semiring R₄]

variable {M : Type*} {N : Type*} {P : Type*} {Q : Type*}

Expand All @@ -225,6 +225,10 @@ variable [Module R M] [Module R₂ N] [Module R₃ P] [Module R₄ Q]

variable [Module R Mₗ] [Module R Nₗ] [Module R Pₗ] [Module R Qₗ] [Module R Qₗ']

variable [SMulCommClass R R M] [SMulCommClass R R Mₗ] [SMulCommClass R R Nₗ] [SMulCommClass R R Pₗ]
[SMulCommClass R R Qₗ] [SMulCommClass R R Qₗ'] [SMulCommClass R₃ R₃ P]
[SMulCommClass R₄ R₄ Q]

variable {σ₁₂ : R →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R →+* R₃}

variable {σ₄₂ : R₄ →+* R₂} {σ₄₃ : R₄ →+* R₃}
Expand Down Expand Up @@ -385,7 +389,8 @@ variable (R M)
/-- Scalar multiplication as a bilinear map `R → M → M`. -/
def lsmul : R →ₗ[R] M →ₗ[R] M :=
mk₂ R (· • ·) add_smul (fun _ _ _ => mul_smul _ _ _) smul_add fun r s m => by
simp only [smul_smul, smul_eq_mul, mul_comm]
simp only
rw [smul_comm]
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#align linear_map.lsmul LinearMap.lsmul

variable {R M}
Expand All @@ -394,7 +399,7 @@ variable {R M}
theorem lsmul_apply (r : R) (m : M) : lsmul R M r m = r • m := rfl
#align linear_map.lsmul_apply LinearMap.lsmul_apply

end CommSemiring
end SMulCommSemiring

section CommRing

Expand Down