#[global]
Hint Resolve lt_wf: arith.
#[global]
Hint Resolve well_founded_lt_compat: arith.
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.

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