Section gd1b.
Hypothesis p2 : IN (PAIR X Y) G.
Let step3 : IN X (Domain G).
Proof Domain_th1 G X Y p2.
Proof union_th2 (Domain F) (Domain G) X step3.
End gd1b.
Proof
union_th4 (IN X (union (Domain F) (Domain G))) F G
(PAIR X Y) step1 gd1a_Out gd1b_Out.
End glueing_domain1.

Theorem glueing_th2 :
forall F G : Ens, SUB (Domain (union F G)) (union (Domain F) (Domain G)).