Definition Fix (x:A) := Fix_F (Rwf x).
(** Proof that [well_founded_induction] satisfies the fixpoint equation. It requires an extra property of the functional *)
Hypothesis
F_ext :
forall (x:A) (f g:forall y:A, R y x -> P y),
(forall (y:A) (p:R y x), f y p = g y p) -> F f = F g.

Lemma Fix_eq : forall x:A, Fix x = F (fun (y:A) (p:R y x) => Fix y).
End FixPoint.