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 Th41:
  L~SpStSeq S = (LSeg(NW-corner S,NE-corner S) \/ LSeg(NE-corner S
,SE-corner S)) \/ (LSeg(SE-corner S,SW-corner S) \/ LSeg(SW-corner S,NW-corner
  S))
proof
  len<*NW-corner S,NE-corner S,SE-corner S*> = 3 by FINSEQ_1:45;
  then
A1: <*NW-corner S,NE-corner S,SE-corner S*>/. len<*NW-corner S,NE-corner S,
  SE-corner S*> = SE-corner S by FINSEQ_4:18;
  <*SW-corner S,NW-corner S*>/.1 = SW-corner S by FINSEQ_4:17;
  hence L~SpStSeq S = L~<*NW-corner S,NE-corner S,SE-corner S*> \/ LSeg(
  SE-corner S,SW-corner S) \/ L~<*SW-corner S,NW-corner S*> by A1,SPPOL_2:23
    .= L~<*NW-corner S,NE-corner S,SE-corner S*> \/ LSeg(SE-corner S,
  SW-corner S) \/ LSeg(SW-corner S,NW-corner S) by SPPOL_2:21
    .= LSeg(NW-corner S,NE-corner S) \/ LSeg(NE-corner S,SE-corner S) \/
  LSeg(SE-corner S,SW-corner S) \/ LSeg(SW-corner S,NW-corner S) by Th8
    .= (LSeg(NW-corner S,NE-corner S) \/ LSeg(NE-corner S,SE-corner S)) \/ (
LSeg(SE-corner S,SW-corner S) \/ LSeg(SW-corner S,NW-corner S)) by XBOOLE_1:4;
end;
