End gd2A.
Section gd2B.
Hypothesis x1 : IN X (Domain G).
Let Y := EV G X.
Let step1 : IN (PAIR X Y) G.
Proof EV_th1 G X x1.
Let step2 : IN (PAIR X Y) H.
Proof union_th2 F G (PAIR X Y) step1.

Lemma gd2B_Out : IN X (Domain H).
Proof Domain_th1 H X Y step2.