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 X = S-max X implies S-most X = {S-min X}
proof
  assume S-min X = S-max X;
  then S-most X c= LSeg(S-min X, S-min X) by Th56;
  then S-most X c= {S-min X} by RLTOPSP1:70;
  hence thesis by ZFMISC_1:33;
end;
