Theorems · Theorem · group theory

QuotientAddGroup.map_surjective_of_surjective

∀ {G : Type u_1} {H : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup H] (N : AddSubgroup G) [nN : N.Normal]
  (M : AddSubgroup H) [inst_2 : M.Normal] (f : G →+ H),
  Function.Surjective (QuotientAddGroup.mk ∘ ⇑f) →
    ∀ (h : N ≤ AddSubgroup.comap f M), Function.Surjective ⇑(QuotientAddGroup.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

AddGroupAddGroupAddSubgroup.NormalAddSubgroup.Normal