proposition: Lemma eqEcard A B : (A == B) = (A \subset B) && (#|B| <= #|A|).
proof: Proof. rewrite eqEsubset; apply: andb_id2l => sAB. by rewrite (geq_leqif (subset_leqif_card sAB)). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)