Definition inv_lt_rel x y := exists2 n, F x n & (forall m, F y m -> n < m).Remark acc_lt_rel : forall x:A, (exists n, F x n) -> Acc R x.

(* Specifications: *)
Theorem well_founded_inv_lt_rel_compat : well_founded R.
Lemma well_founded_inv_rel_inv_lt_rel (A:Set) (F:A -> nat -> Prop) : well_founded (inv_lt_rel A F).