instMulActionOfIsScalarTower — Mathlib

English

Another variant asserting central scalar compatibility in the localized setting.

Русский

Другая вариация утверждает совместимость центрального скаляра в локализованной структуре.

LaTeX

$$$\\text{IsCentralScalar}(R,X[S^{-1}]).$$$

Lean4

@[to_additive]
instance {R} [Monoid R] [MulAction R M] [IsScalarTower R M M] [MulAction R X] [IsScalarTower R M X] : MulAction R X[S⁻¹]
    where
  one_smul :=
    OreLocalization.ind fun x s ↦ by rw [← smul_one_oreDiv_one_smul, one_smul, ← OreLocalization.one_def, one_smul]
  mul_smul s₁ s₂ x := by rw [← smul_eq_mul, smul_assoc]

Похожие утверждения