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

theorem
  x = {} & y <> {} implies x - y = [{},y]
proof
  assume that
A1: x = {} and
A2: y <> {};
  x <=' y by A1,Th6;
  then not y <=' x by A1,A2,Th4;
  hence x - y =[{},y -' x] by Def2
    .= [{},y] by A1,Lm4;
end;
