reserve a, b for Real,
  r for Real,
  rr for Real,
  i, j, n for Nat,
  M for non empty MetrSpace,
  p, q, s for Point of TOP-REAL 2,
  e for Point of Euclid 2,
  w for Point of Euclid n,
  z for Point of M,
  A, B for Subset of TOP-REAL n,
  P for Subset of TOP-REAL 2,
  D for non empty Subset of TOP-REAL 2;
reserve a, b for Real;
reserve a, b for Real;
reserve r for Real;

theorem Th63:
  for M being Reflexive symmetric triangle non empty MetrStruct,
  X, Y being Subset of M st the carrier of M = X \/ Y & M is non bounded & X is
  bounded holds Y is non bounded
proof
  let M be Reflexive symmetric triangle non empty MetrStruct, X, Y be Subset
  of M such that
A1: the carrier of M = X \/ Y and
A2: M is non bounded;
  assume that
A3: X is bounded and
A4: Y is bounded;
  [#]M is bounded by A1,A3,A4,TBSP_1:13;
  hence thesis by A2,TBSP_1:18;
end;
