Mathlib Map

Theorems · Theorem · group theory

MulDistribMulAction.smul_mul

∀ {M : Type u_9} {N : Type u_10} {inst : Monoid M} {inst_1 : Monoid N} [self : MulDistribMulAction M N] (r : M)
  (x y : N), r • (x * y) = r • x * r • y

Distributivity of • across *

Defined in
Mathlib.Algebra.Group.Action.Defs
Cited by
1 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
MulDistribMulAction
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

smul_mul' · cited by 7smul_mul'Monoid · cited by 3887MonoidMulDistribMulAction · cited by 120MulDistribMulActionMulDistribMulAction.smul_mulCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.