Section WellOrdering.
Variable A : Type.
Variable B : A -> Type.
Notation WO := (WO A B).
Inductive le_WO : WO -> WO -> Prop :=
le_sup : forall (a:A) (f:B a -> WO) (v:B a), le_WO (f v) (sup _ _ a f).

Theorem wf_WO : well_founded le_WO.