proposition: Lemma quotientDG A G : H \subset G -> (A :\: G) / H = A / H :\: G / H.
proof: Proof. by rewrite -{1}ker_coset; apply: morphimDG. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)