reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;

theorem Th15:
  for x being object
  for f being Function of X,Y, g being Function st Y <> {} & x in
  X holds (g*f).x = g.(f.x)
proof let x be object;
  let f be Function of X,Y, g be Function;
  assume Y <> {};
  then X = dom f by Def1;
  hence thesis by FUNCT_1:13;
end;
