Theorems · Theorem · group theory

AddSubmonoid.map_iInf

∀ {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] {ι : Sort u_5} [Nonempty ι] (f : F),
  Function.Injective ⇑f → ∀ (s : ι → AddSubmonoid M), AddSubmonoid.map f (iInf s) = ⨅ i, AddSubmonoid.map f (s i)

Defined in

Mathlib.Algebra.Group.Submonoid.Operations

Cited by

0 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddZeroClassAddZeroClassFunLikeAddMonoidHomClassNonempty