Theorems · Theorem · commutative algebra

map_inv_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 : DivisionSemiring R] [inst_5 : DivisionSemiring S] [inst_6 : Module R M] [inst_7 : Module S M₂] (n : ℕ)
  (x : M), f ((↑n)⁻¹ • x) = (↑n)⁻¹ • f x

Defined in

Mathlib.Algebra.Module.Basic

Cited by

8 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidAddCommMonoidFunLikeAddMonoidHomClassDivisionSemiringDivisionSemiringModuleModule