instMulActionWithZeroSubtypeMem — Mathlib

English

If S ⊆ R' is a subsemiring and α has a MulActionWithZero by R', then α inherits MulActionWithZero by S on the restricted subtype; the zero-action axioms carry over.

Русский

Если S ⊆ R' является подsemiring и α имеет MulActionWithZero по R', то α наследует MulActionWithZero по S на ограниченном подтипе; аксиомы нулевого действия сохраняются.

LaTeX

$$$MulActionWithZero S \ α$$$

Lean4

instance (priority := low) {S' : Type*} [SetLike S' R'] [SubsemiringClass S' R'] (s : S') [Zero α]
    [MulActionWithZero R' α] : MulActionWithZero s α
    where
  smul_zero r := smul_zero (r : R')
  zero_smul := zero_smul R'

Похожие утверждения