Section Inverse_Image.
Variables A B : Type.
Variable R : B -> B -> Prop.
Variable f : A -> B.
Let Rof (x y:A) : Prop := R (f x) (f y).
Remark Acc_lemma : forall y:B, Acc R y -> forall x:A, y = f x -> Acc Rof x.
Variable F : A -> B -> Prop.
Let RoF (x y:A) : Prop :=
exists2 b : B, F x b & (forall c:B, F y c -> R b c).

Lemma Acc_inverse_rel : forall b:B, Acc R b -> forall x:A, F x b -> Acc RoF x.