theorem
  p in LSeg(p1,p2) & LSeg(p1,p2) is horizontal implies LSeg(p,p2) is horizontal
proof
  assume
A1: p in LSeg(p1,p2);
  assume
A2: LSeg(p1,p2) is horizontal;
  then
A3: p1`2 = p2`2 by SPPOL_1:15;
  p1 in LSeg(p1,p2) by RLTOPSP1:68;
  then p`2 = p1`2 by A1,A2;
  hence thesis by A3,SPPOL_1:15;
end;
