Section LT_WF_REL.
Variable A : Set.
Variable R : A -> A -> Prop.
(* Relational form of inversion *)
Variable F : A -> nat -> Prop.
Definition inv_lt_rel x y := exists2 n, F x n & (forall m, F y m -> n < m).
Hypothesis F_compat : forall x y:A, R x y -> inv_lt_rel x y.
Remark acc_lt_rel : forall x:A, (exists n, F x n) -> Acc R x.
End LT_WF_REL.

Lemma well_founded_inv_rel_inv_lt_rel :
forall (A:Set) (F:A -> nat -> Prop), well_founded (inv_lt_rel A F).