
theorem
  for V being non empty addLoopStr, M,N being non empty Subset of V
  holds M + N is non empty
proof
  let V be non empty addLoopStr;
  let M,N be non empty Subset of V;
  consider x be object such that
A1: x in M by XBOOLE_0:def 1;
  consider y be object such that
A2: y in N by XBOOLE_0:def 1;
  reconsider x,y as Element of V by A1,A2;
  x + y in {u + v where u,v is Element of V: u in M & v in N} by A1,A2;
  hence thesis by RUSUB_4:def 9;
end;
