Theorems · Theorem · group theory

QuotientGroup.congr_apply

∀ {G : Type u_1} {H : Type u_2} [inst : Group G] [inst_1 : Group H] (G' : Subgroup G) (H' : Subgroup H)
  [inst_2 : G'.Normal] [inst_3 : H'.Normal] (e : G ≃* H) (he : Subgroup.map (↑e) G' = H') (x : G),
  (QuotientGroup.congr G' H' e he) ↑x = (QuotientGroup.mk' H') (e x)

Defined in

Mathlib.GroupTheory.QuotientGroup.Defs

Cited by

0 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupGroupSubgroup.NormalSubgroup.Normal