theorem Th45:
  (SE-corner P)`1 = (E-min P)`1 & (SE-corner P)`1 = (E-max P)`1 &
  (E-min P)`1 = (E-max P)`1 & (E-min P)`1 = (NE-corner P)`1 & (E-max P)`1 = (
  NE-corner P)`1
proof
  (E-min P)`1 = E-bound P & (E-max P)`1 = E-bound P by EUCLID:52;
  hence thesis by EUCLID:52;
end;
