theorem Th68:
  S-most L~SpStSeq C = LSeg(SW-corner C,SE-corner C)
proof
  set X = L~SpStSeq C;
  set S3 = LSeg(SE-corner C,SW-corner C), S4 = LSeg(SW-corner C,NW-corner C);
A1: S3 c= S3 \/ S4 by XBOOLE_1:7;
  X = (LSeg(NW-corner C,NE-corner C) \/ LSeg(NE-corner C,SE-corner C)) \/
  (S3 \/ S4) by Th41;
  then
A2: S3 \/ S4 c= X by XBOOLE_1:7;
  LSeg(SW-corner X, SE-corner X) = LSeg(SW-corner X, SE-corner C) by Th65
    .= LSeg(SW-corner C,SE-corner C) by Th64;
  hence thesis by A1,A2,XBOOLE_1:1,28;
end;
