Section cartpair.
Variable A B X Y : Ens.
Hypothesis i : IN (PAIR X Y) (Cartesian A B).
Let U := PAIR X Y.
Let X1 := PR1 U.
Let Y1 := PR2 U.
Let step1 : EQ X X1.
Proof PAIR_proj_th3 X Y.
Let step2 : IN X1 A.
Proof Cartesian_proj1_th A B U i.

Lemma cartpairA_Out : IN X A.