Theorems · Theorem · commutative algebra

map_natCast_smul

∀ {M : Type u_3} {M₂ : Type u_4} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂] {F : Type u_5}
  [inst_2 : FunLike F M M₂] [AddMonoidHomClass F M M₂] (f : F) (R : Type u_6) (S : Type u_7) [inst_4 : Semiring R]
  [inst_5 : Semiring S] [inst_6 : Module R M] [inst_7 : Module S M₂] (x : ℕ) (a : M), f (↑x • a) = ↑x • f a

Defined in

Mathlib.Algebra.Module.NatInt

Cited by

3 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext

Assumes

AddCommMonoidAddCommMonoidFunLikeAddMonoidHomClassSemiringSemiringModuleModule