(* The cartesian product and its properties *)


(* This definition of the ordered pair is slightly different from *)
(* the usual one, since we want it to work in an intuisionistic   *)
(* setting. Works the same, neitherless. The soundness proofs are *)
(* unpleasant.                                                    *)


Definition Couple (E E' : Ens) := Paire (Sing E) (Paire Vide (Sing E')).

(* Specifications: *)
Theorem Couple_inj_left : forall A A' B B' : Ens, EQ (Couple A A') (Couple B B') -> EQ A B.
Theorem Couple_inj_right : forall A A' B B' : Ens, EQ (Couple A A') (Couple B B') -> EQ A' B'.