Section Well_founded_Nat.
Variable A : Type.
Variable f : A -> nat.
Definition ltof (a b:A) := f a < f b.
Definition gtof (a b:A) := f b > f a.

Lemma gt_wf_rec :
forall n (P:nat -> Set), (forall n, (forall m, n > m -> P m) -> P n) -> P n.