theorem Th32:
  LSeg(UMP P, |[ (W-bound P + E-bound P) / 2, N-bound P]|) is vertical
proof
  set w = (W-bound P + E-bound P) / 2;
  |[w,N-bound P]|`1 = w & (UMP P)`1 = w by EUCLID:52;
  hence thesis by SPPOL_1:16;
end;
