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

Lemma sol_coprime_Sylow_trans A G :
solvable A -> A \subset 'N(G) -> coprime #|G| #|A| ->
[transitive 'C_G(A), on [set P in 'Syl_p(G) | A \subset 'N(P)] | 'JG].