Proof glueing_domain1_Out.
Section glueing_domain2.
Variable F G X : Ens.
Hypothesis x : IN X (union (Domain F) (Domain G)).
Let H := union F G.
Section gd2A.
Hypothesis x1 : IN X (Domain F).
Let Y := EV F X.
Let step1 : IN (PAIR X Y) F.
Proof EV_th1 F X x1.
Let step2 : IN (PAIR X Y) H.
Proof union_th1 F G (PAIR X Y) step1.

Lemma gd2A_Out : IN X (Domain H).
Proof Domain_th1 H X Y step2.