reserve x,y,z for Element of REAL+;

theorem
  z <=' y implies x *' (y -' z) = (x *' y) - (x *' z)
proof
  assume z <=' y;
  then x *' z <=' x *' y by Th8;
  then (x *' y) - (x *' z) = (x *' y) -' (x *' z) by Def2;
  hence thesis by Lm14;
end;
