Theorems · Theorem · group theory

QuotientGroup.map_surjective_of_surjective

∀ {G : Type u_1} {H : Type u_2} [inst : Group G] [inst_1 : Group H] (N : Subgroup G) [nN : N.Normal] (M : Subgroup H)
  [inst_2 : M.Normal] (f : G →* H),
  Function.Surjective (QuotientGroup.mk ∘ ⇑f) →
    ∀ (h : N ≤ Subgroup.comap f M), Function.Surjective ⇑(QuotientGroup.map N M f h)

Defined in

Mathlib.GroupTheory.QuotientGroup.Defs

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupGroupSubgroup.NormalSubgroup.Normal