proposition: Corollary Hall_exists pi (G : {group gT}) : solvable G -> exists H : {group gT}, pi.-Hall(G) H.
proof: Proof. by case/(Hall_exists_subJ pi) => H; exists H. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div choice) mathcomp(fintype finset prime fingroup morphism) mathcomp(automorphism quotient action gproduct gfunctor) mathcomp(commutator center pgroup finmodule nilpotent) mathcomp(sylow abelian maximal)