Remark Acc_lemma : forall y:B, Acc R y -> forall x:A, y = f x -> Acc Rof x.

(* Specifications: *)
Lemma Acc_inverse_image : forall x:A, Acc R (f x) -> Acc Rof x.
Theorem wf_inverse_image : well_founded R -> well_founded Rof.
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.
Lemma wf_simulation (Q : A -> A -> Prop) : well_founded R -> (forall a1 a2, Q a2 a1 -> exists b2, F a2 b2) -> (forall a1 a2 b1, Q a2 a1 -> F a1 b1 -> exists b2, F a2 b2 /\ R b2 b1) -> well_founded Q.
Lemma Acc_inverse_rel : forall b:B, Acc R b -> forall x:A, F x b -> Acc RoF x.
Theorem wf_inverse_rel : well_founded R -> well_founded RoF.