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;

theorem
  LSeg(SW-corner P,SE-corner P) c= L~SpStSeq P
proof
  LSeg(NW-corner P,NE-corner P) \/ LSeg(NE-corner P,SE-corner P) \/ LSeg(
SE-corner P,SW-corner P) c= LSeg(NW-corner P,NE-corner P) \/ LSeg(NE-corner P,
SE-corner P) \/ LSeg(SE-corner P,SW-corner P) \/ LSeg(SW-corner P,NW-corner P)
  by XBOOLE_1:7;
  then
A1: LSeg(NW-corner P,NE-corner P) \/ LSeg(NE-corner P,SE-corner P) \/ LSeg(
SE-corner P,SW-corner P) c= LSeg(NW-corner P,NE-corner P) \/ LSeg(NE-corner P,
SE-corner P) \/ (LSeg(SE-corner P,SW-corner P) \/ LSeg(SW-corner P,NW-corner P)
  ) by XBOOLE_1:4;
  LSeg(SW-corner P,SE-corner P) c= (LSeg(NW-corner P,NE-corner P) \/ LSeg(
  NE-corner P,SE-corner P)) \/ LSeg(SW-corner P,SE-corner P) by XBOOLE_1:7;
  then
  LSeg(SW-corner P,SE-corner P) c= (LSeg(NW-corner P,NE-corner P) \/ LSeg(
NE-corner P,SE-corner P)) \/ (LSeg(SE-corner P,SW-corner P) \/ LSeg(SW-corner P
  ,NW-corner P)) by A1;
  hence thesis by SPRECT_1:41;
end;
