End ExternalAction.
Section SylowSolvableAct.
Variables (gT : finGroupType) (p : nat).
Implicit Types A B G X : {group gT}.

Lemma sol_coprime_Sylow_exists A G :
solvable A -> A \subset 'N(G) -> coprime #|G| #|A| ->
exists2 P : {group gT}, p.-Sylow(G) P & A \subset 'N(P).