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 Th56:
  S-most X c= LSeg(S-min X, S-max X)
proof
  let x be object;
  assume
A1: x in S-most X;
  then reconsider p = x as Point of TOP-REAL 2;
A2: p`1 <=(S-max X)`1 by A1,Th55;
A3: (S-min X)`2 = (S-max X)`2 by Th53;
  p`2 = (S-min X)`2 & (S-min X)`1 <= p`1 by A1,Th55;
  hence thesis by A3,A2,GOBOARD7:8;
end;
