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
  S-min P = W-min P implies S-min P = SW-corner P
proof
A1: (S-min P)`2 = S-bound P by EUCLID:52;
  assume S-min P = W-min P;
  hence thesis by A1,EUCLID:52;
end;
