proposition: Lemma cosetpreSK C D : (coset H @*^-1 C \subset coset H @*^-1 D) = (C \subset D).
proof: Proof. by rewrite morphpreSK ?sub_im_coset. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)