proposition: Lemma card_Hall pi G H : pi.-Hall(G) H -> #|H| = #|G|`_pi.
proof: Proof. case/and3P=> sHG piH pi'H; rewrite -(Lagrange sHG). by rewrite partnM ?Lagrange // part_pnat_id ?part_p'nat ?muln1. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset prime fingroup morphism) mathcomp(gfunctor automorphism quotient action gproduct) mathcomp(cyclic)