reserve A for set,
  C for non empty set,
  B for Subset of A,
  x for Element of A,
  f,g for Function of A,C;

theorem Th4:
  g|B +* f = f
proof
  dom (g|B) = B & dom f = A by Th1,FUNCT_2:def 1;
  hence thesis by FUNCT_4:19;
end;
