Section Image.
Inductive Im (R : Relation U) (A : Ensemble U) (y : U) : Prop :=
Im_intro : forall x : U, R x y -> In U A x -> Im R A y.

Lemma Im_stable_par_incl :
forall (R : Relation U) (A1 A2 : Ensemble U),
Included U A1 A2 -> Included U (Im R A1) (Im R A2).