proposition: Lemma ltn_quotient A : H :!=: 1 -> H \subset A -> #|A / H| < #|A|.
proof: Proof. by move=> ntH sHA; rewrite ltn_morphim // ker_coset (setIidPr sHA) proper1G. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)