Let RoF (x y:A) : Prop :=
exists2 b : B, F x b & (forall c:B, F y c -> R b c).

(* Specifications: *)
Lemma Acc_simulation (Q : A -> A -> Prop) :
forall b, Acc R b ->
(forall a1 a2 b1, Q a2 a1 -> F a1 b1 -> exists b2, F a2 b2 /\ R b2 b1) ->
forall a, F a b -> Acc Q a.
Theorem wf_inverse_rel : well_founded R -> well_founded RoF.
End Inverse_Image.