
theorem Th12:
  for V being RealLinearSpace, M being non empty Subset of V holds 0.V in M - M
proof
  let V be RealLinearSpace;
  let M be non empty Subset of V;
  consider v being object such that
A1: v in M by XBOOLE_0:def 1;
  reconsider v as Element of V by A1;
  v - v in {u1 - v1 where u1,v1 is Element of V : u1 in M & v1 in M} by A1;
  hence thesis by RLVECT_1:15;
end;
