reserve r, s, t, g for Real,

          r3, r1, r2, q3, p3 for Real;
reserve T for TopStruct,
  f for RealMap of T;
reserve p for Point of TOP-REAL 2,
  P for Subset of TOP-REAL 2,
  Z for non empty Subset of TOP-REAL 2,
  X for non empty compact Subset of TOP-REAL 2;

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;
