proposition: Lemma quotient_setIpre A D : (A :&: coset H @*^-1 D) / H = A / H :&: D.
proof: Proof. exact: morphim_setIpre. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)