A10: dom g = X by FUNCT_2:def 1;
A11: dom (gt (f,g)) = (dom f) /\ (dom g) by Def6;
A12: dom f = X by FUNCT_2:def 1;
rng (gt (f,g)) c= INT ;
hence gt (f,g) is Function of X,INT by A11, A12, A10, FUNCT_2:2; :: thesis: verum