unfold Paire in |- *.
simpl in |- *.
intros; split.
simple induction x.
exists true; auto with zfc.
exists false; auto with zfc.
simple induction y; simpl in |- *.
exists true; auto with zfc.
exists false; auto with zfc.
Qed.

(* Specifications: *)
Theorem Paire_sound_right :
forall A B B' : Ens, EQ B B' -> EQ (Paire A B) (Paire A B').
Theorem Paire_sound_right :
forall A B B' : Ens, EQ B B' -> EQ (Paire A B) (Paire A B').
Theorem Paire_sound_rightC :
forall A B B' : Ens, EQC B B' -> EQC (Paire A B) (Paire A B').
Theorem Paire_sound_rightC :
forall A B B' : Ens, EQC B B' -> EQC (Paire A B) (Paire A B').