reserve i for Integer,
  a, b, r, s for Real;

theorem
  for X being TopStruct, Y being non empty TopStruct, Z being non empty
  SubSpace of Y, f being Function of X,Z holds f is Function of X,Y
proof
  let X be TopStruct, Y be non empty TopStruct, Z be non empty SubSpace of Y;
  let f be Function of X,Z;
  the carrier of Z is Subset of Y by TSEP_1:1;
  then
A1: rng f c= the carrier of Y by XBOOLE_1:1;
  dom f = the carrier of X by FUNCT_2:def 1;
  hence thesis by A1,FUNCT_2:2;
end;
