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.
Proof Domain_th1 H X Y step2.
End gd2B.
Proof union_th4 (IN X (Domain H)) (Domain F) (Domain G) X x gd2A_Out gd2B_Out.
End glueing_domain2.

Theorem glueing_th3 :
forall F G : Ens, SUB (union (Domain F) (Domain G)) (Domain (union F G)).