simple induction E''; unfold CINC in |- *; simpl in |- *;
intros A f XR e X1 E0 i; apply X1.
apply CIN_sound_right with E'; auto with zfc.
Qed.

(* Specifications: *)
Theorem CINC_sound_right :
forall E E' E'' : Ens, EQC E' E'' -> CINC E E' -> CINC E E''.
Theorem CINC_sound_right :
forall E E' E'' : Ens, EQC E' E'' -> CINC E E' -> CINC E E''.