Theorems · Theorem · ring theory

LinearMapClass.map_smul

∀ {R : outParam (Type u_14)} {M : outParam (Type u_15)} {M₂ : outParam (Type u_16)} [inst : Semiring R]
  [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid M₂] [inst_3 : Module R M] [inst_4 : Module R M₂] {F : Type u_17}
  [inst_5 : FunLike F M M₂] [LinearMapClass F R M M₂] (f : F) (r : R) (x : M), f (r • x) = r • f x

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

4 results in Mathlib

Foundations

Depth 17 from the axioms · uses no axioms

Assumes

SemiringAddCommMonoidAddCommMonoidModuleModuleFunLikeLinearMapClass