proposition: Lemma rankS A B : A \subset B -> 'r(A) <= 'r(B).
proof: Proof. move=> sAB; rewrite /rank !big_mkord; apply/bigmax_leqP=> p _. have leAB: #|A| < #|B|.+1 by rewrite ltnS subset_leq_card. by rewrite (bigmax_sup (widen_ord leAB p)) ?p_rankS. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path choice) mathcomp(div fintype finfun bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism action) mathcomp(quotient gfunctor gproduct ssralg countalg finalg zmodp) mathcomp(cyclic pgroup gseries nilpotent sylow)