reserve r,s,t,u for Real;

theorem Th3:
  for X being non empty addLoopStr, M,N being Subset of X, x,y
  being Point of X st x in M & y in N holds x+y in M+N
proof
  let X be non empty addLoopStr, M,N be Subset of X, x,y be Point of X;
  M+N = {u + v where u,v is Point of X: u in M & v in N} by RUSUB_4:def 9;
  hence thesis;
end;
