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