Section gr2.
Hypothesis x2 : IN X G.
Proof g X x2.
End gr2.
Proof union_th4 (is_a_pair X) F G X x gr1_Out gr2_Out.
End glueing_relation_proof.

Theorem glueing_th1 :
forall (F G : Ens) (f : is_a_relation F) (g : is_a_relation G),
is_a_relation (union F G).