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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(* 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.