
theorem
  for T being non empty TopSpace, p being Point of T for A, B being
  Element of OpenNeighborhoods p holds A \/ B is Element of OpenNeighborhoods p
proof
  let T be non empty TopSpace, p be Point of T, A, B be Element of
  OpenNeighborhoods p;
  consider W being Subset of T such that
A1: W = A and
A2: p in W and
A3: W is open by YELLOW_6:29;
A4: p in A \/ B by A1,A2,XBOOLE_0:def 3;
  consider X being Subset of T such that
A5: X = B and
  p in X and
A6: X is open by YELLOW_6:29;
  W \/ X is open by A3,A6;
  hence thesis by A1,A5,A4,YELLOW_6:30;
end;
