reserve S for Subset of TOP-REAL 2,
  C,C1,C2 for non empty compact Subset of TOP-REAL 2,
  p,q for Point of TOP-REAL 2;
reserve i,j,k for Nat,
  t,r1,r2,s1,s2 for Real;
reserve D1 for non vertical non empty compact Subset of TOP-REAL 2,
  D2 for non horizontal non empty compact Subset of TOP-REAL 2,
  D for non vertical non horizontal non empty compact Subset of TOP-REAL 2;

theorem Th42:
  L~SpStSeq D = [.W-bound D,E-bound D,S-bound D,N-bound D.]
proof
  L~SpStSeq D = (LSeg(NW-corner D,NE-corner D) \/ LSeg(NE-corner D,
SE-corner D)) \/ (LSeg(SE-corner D,SW-corner D) \/ LSeg(SW-corner D,NW-corner D
  )) by Th41
    .= LSeg(SW-corner D,NW-corner D) \/ ( LSeg(NW-corner D,NE-corner D) \/
LSeg(NE-corner D,SE-corner D) ) \/ LSeg(SE-corner D,SW-corner D) by XBOOLE_1:4
    .= LSeg(SW-corner D,NW-corner D) \/ LSeg(NW-corner D,NE-corner D) \/
  LSeg(NE-corner D,SE-corner D) \/ LSeg(SE-corner D,SW-corner D) by XBOOLE_1:4
    .= ( LSeg(SW-corner D,NW-corner D) \/ LSeg(NW-corner D,NE-corner D) ) \/
( LSeg(NE-corner D,SE-corner D) \/ LSeg(SE-corner D,SW-corner D) ) by
XBOOLE_1:4;
  hence thesis by SPPOL_2:def 3;
end;
