theorem
  p in LSeg(p1,p2) & LSeg(p1,p2) is vertical implies LSeg(p,p2) is vertical
proof
  assume
A1: p in LSeg(p1,p2);
  assume
A2: LSeg(p1,p2) is vertical;
  then
A3: p1`1 = p2`1 by SPPOL_1:16;
  p1 in LSeg(p1,p2) by RLTOPSP1:68;
  then p`1 = p1`1 by A1,A2;
  hence thesis by A3,SPPOL_1:16;
end;
