instDistribMulActionOfSMulCommClass

English

If the base actions form a distributive multiplication action, then the function space X →ₑ[σ] Y inherits a distributive action by the same ring.

Русский

Если базовые действия образуют распределимое действие, то пространство функций X→ₑ[σ]Y наследует такое же распределительное действие.

LaTeX

$$$\text{DistribMulAction } R (X \to_{\sigma} Y)$ with induced action by $R$.$$

Lean4

instance [AddMonoid Y] [Monoid R] [SMul M X] [DistribSMul N Y] [DistribMulAction R Y] [SMulCommClass N R Y] :
    DistribMulAction R (X →ₑ[σ] Y) where
  __ := inferInstanceAs (MulAction _ _)
  __ := inferInstanceAs (DistribSMul _ _)

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