theorem Th2:
  for f,g,h being Function st f \/ g = h
   for x being object st x in dom f /\ dom g holds f.x = g.x
proof
  let f,g,h be Function such that
A1: f \/ g = h;
  let x be object;
  assume
A2: x in dom f /\ dom g;
  then x in dom f by XBOOLE_0:def 4;
  then
A3: h.x = f.x by A1,GRFUNC_1:15;
  x in dom g by A2,XBOOLE_0:def 4;
  hence thesis by A1,A3,GRFUNC_1:15;
end;
