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