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 Th69:
  E-most L~SpStSeq C = LSeg(SE-corner C,NE-corner C)
proof
  set X = L~SpStSeq C;
  set S1 = LSeg(NW-corner C,NE-corner C), S2 = LSeg(NE-corner C,SE-corner C);
A1: S2 c= S1 \/ S2 by XBOOLE_1:7;
  X = (S1 \/ S2) \/ (LSeg(SE-corner C,SW-corner C) \/ LSeg(SW-corner C,
  NW-corner C)) by Th41;
  then
A2: S1 \/ S2 c= X by XBOOLE_1:7;
  LSeg(SE-corner X, NE-corner X) = LSeg(SE-corner X, NE-corner C) by Th63
    .= LSeg(SE-corner C,NE-corner C) by Th65;
  hence thesis by A1,A2,XBOOLE_1:1,28;
end;
