(* R is well-founded if and only if every nonempty subset of
   T has a minimal element *)

Definition minimal_element_property : Prop :=
  forall S:Ensemble T, Inhabited S -> exists x:T, In S x /\
    forall y:T, In S y -> ~ R y x.

Lemma MEP_implies_WF: minimal_element_property -> well_founded R.