reserve C for Simple_closed_curve,
  P for Subset of TOP-REAL 2,
  p for Point of TOP-REAL 2,
  n for Element of NAT;
reserve D for compact with_the_max_arc Subset of TOP-REAL 2;

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;
