Theorems · Theorem · group theory

AddMonoidHom.map_mclosure

∀ {M : Type u_1} {N : Type u_2} [inst : AddZeroClass M] [inst_1 : AddZeroClass N] {F : Type u_4}
  [inst_2 : FunLike F M N] [mc : AddMonoidHomClass F M N] (f : F) (s : Set M),
  AddSubmonoid.map f (AddSubmonoid.closure s) = AddSubmonoid.closure (⇑f '' s)

The image under an AddMonoidHom of the AddSubmonoid generated by a set equals the AddSubmonoid generated by the image of the set.

Defined in

Mathlib.Algebra.Group.Submonoid.Operations

Cited by

12 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddZeroClassAddZeroClassFunLikeAddMonoidHomClass