toMulActionWithZero — Mathlib

English

A module over a semiring automatically inherits a MulActionWithZero structure; the actions satisfy smul_zero and zero_smul laws.

Русский

Модуль над полупрямой полугруппой автоматически наследует структуру MulActionWithZero; выполнены законы smul_zero и zero_smul.

LaTeX

$$Module.toMulActionWithZero$$

Lean4

/-- A module over a semiring automatically inherits a `MulActionWithZero` structure. -/
instance (priority := 100) toMulActionWithZero {R M} {_ : Semiring R} {_ : AddCommMonoid M} [Module R M] :
    MulActionWithZero R M :=
  { (inferInstance : MulAction R M) with
    smul_zero := smul_zero
    zero_smul := Module.zero_smul }

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