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 Th33:
  LSeg(SW-corner D1,NW-corner D1) misses LSeg(SE-corner D1, NE-corner D1)
proof
  assume
  LSeg(SW-corner D1,NW-corner D1) /\ LSeg(SE-corner D1,NE-corner D1) <> {};
  then consider a being object such that
A1: a in LSeg(SW-corner D1,NW-corner D1) /\ LSeg(SE-corner D1,NE-corner
  D1) by XBOOLE_0:def 1;
  a in LSeg(NE-corner D1,SE-corner D1) by A1,XBOOLE_0:def 4;
  then
  a in {p : p`1= E-bound D1 & p`2 <= N-bound D1 & p`2 >= S-bound D1} by Th23;
  then
A2: ex p st p=a & p`1 = E-bound D1 & p`2 <= N-bound D1 & p`2 >= S-bound D1;
  a in LSeg(NW-corner D1,SW-corner D1)by A1,XBOOLE_0:def 4;
  then a in {p : p`1 = W-bound D1 & p`2 <= N-bound D1 & p`2 >= S-bound D1} by
Th26;
  then
  ex p st p = a & p`1 = W-bound D1 & p`2 <= N-bound D1 & p`2 >= S-bound D1;
  hence contradiction by A2,Th15;
end;
