A19: dom g = X by FUNCT_2:def 1;
A20: dom (gt (f,g)) = (dom f) /\ (dom g) by Def6;
A21: dom f = X by FUNCT_2:def 1;
rng (gt (f,g)) c= INT

proof

let y be set ; :: according to TARSKI:def 3 :: thesis: ( not y in rng (gt (f,g)) or y in INT )
assume y in rng (gt (f,g)) ; :: thesis: y in INT
then consider a being set such that
a in dom (gt (f,g)) and
A23: y = (gt (f,g)) . a by FUNCT_1:def 5;
thus y in INT by A23, INT_1:def 2; :: thesis: verum

end;

hence gt (f,g) is Function of X,INT by A20, A21, A19, FUNCT_2:4; :: thesis: verum