
theorem Th5:
  for X being TopStruct,Y,Z being non empty TopStruct,
  f being Function of X,Y, g being Function of X,Z holds dom f=dom g
  & dom f=the carrier of X & dom f=[#]X
proof
  let X be TopStruct,Y,Z be non empty TopStruct,
  f be Function of X,Y, g be Function of X,Z;
  dom f=the carrier of X by FUNCT_2:def 1;
  hence thesis by FUNCT_2:def 1;
end;
