proposition: Lemma injm_rank : 'r(f @* G) = 'r(G).
proof: Proof. apply/eqP; rewrite eqn_leq; apply/andP; split. by have [p _ ->] := rank_witness (f @* G); rewrite injm_p_rank p_rank_le_rank. by have [p _ ->] := rank_witness G; rewrite -injm_p_rank p_rank_le_rank. 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)