Theorems · Theorem · group theory

QuotientAddGroup.map_map

∀ {G : Type u_1} {H : Type u_2} [inst : AddGroup G] [inst_1 : AddGroup H] (N : AddSubgroup G) [nN : N.Normal]
  {I : Type u_5} [inst_2 : AddGroup I] (M : AddSubgroup H) (O : AddSubgroup I) [inst_3 : M.Normal] [inst_4 : O.Normal]
  (f : G →+ H) (g : H →+ I) (hf : N ≤ AddSubgroup.comap f M) (hg : M ≤ AddSubgroup.comap g O)
  (hgf : optParam (N ≤ AddSubgroup.comap (g.comp f) O) ⋯) (x : G ⧸ N),
  (QuotientAddGroup.map M O g hg) ((QuotientAddGroup.map N M f hf) x) = (QuotientAddGroup.map N O (g.comp f) hgf) x

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.NormalAddGroupAddSubgroup.NormalAddSubgroup.Normal