Section DecreasingSequences.
(* R is well-founded if and only if there is no infinite strictly decreasing sequence of elements of T *)
Variable T:Type.
Variable R:relation T.
Definition decreasing_sequence_property :=
forall a:nat->T, exists n:nat, ~ R (a (S n)) (a n).

(* Specifications: *)
Lemma WF_implies_DSP: well_founded R -> decreasing_sequence_property.
Lemma DSP_implies_WF: decreasing_sequence_property -> well_founded R.
End DecreasingSequences.