Section Transitive.
Variable (leT : rel T).
Hypothesis leT_tr : transitive leT.
Let leT_tr' : {in predT & &, transitive leT}. Proof. exact: in3W. Qed.

Lemma cycle_all2rel_in (T : Type) (P : {pred T}) (leT : rel T) :
{in P & &, transitive leT} ->
forall s, all P s -> cycle leT s = all2rel leT s.