
theorem
  for V being non empty addLoopStr, M,N being Subset of V st M is empty
  or N is empty holds M - N is empty
proof
  let V be non empty addLoopStr;
  let M,N be Subset of V;
  assume
A1: M is empty or N is empty;
  assume not M - N is empty;
  then consider x being object such that
A2: x in M - N;
  ex u,v being Element of V st x = u - v & u in M & v in N by A2;
  hence contradiction by A1;
end;
