Section Second_inductive_lemma.
Variable U : Type.
Variable C : Cpo U.
Definition D : PO U := PO_of_cpo U C.
Hint Resolve Triples_are_enough_finite_case.

Theorem Triples_are_enough :
(forall x y z : U,
Consistent U D (Triple U x y z) ->
ex (fun bsup : U => Lub U D (Triple U x y z) bsup)) ->
Coherent U D.