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

theorem
  y -' z <> {} & z <=' y & x <> {} implies (x *' z) - (x *' y) = [{},x
  *' (y -' z)]
proof
  assume y -' z <> {};
  then
A1: y <> z by Lm3;
  assume z <=' y;
  then not y <=' z by A1,Th4;
  hence thesis by Th27;
end;
