Theorems · Theorem · ring theory

LinearMap.smul_apply

∀ {R : Type u_1} {R₂ : Type u_3} {S : Type u_5} {M : Type u_8} {M₂ : Type u_10} [inst : Semiring R]
  [inst_1 : Semiring R₂] [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M]
  [inst_5 : Module R₂ M₂] {σ₁₂ : R →+* R₂} [inst_6 : DistribSMul S M₂] [inst_7 : SMulCommClass R₂ S M₂] (a : S)
  (f : M →ₛₗ[σ₁₂] M₂) (x : M), (a • f) x = a • f x

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

15 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleDistribSMulSMulCommClass