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 Th32:
  W-most X c= LSeg(W-min X, W-max X)
proof
  let x be object;
  assume
A1: x in W-most X;
  then reconsider p = x as Point of TOP-REAL 2;
A2: p`2 <=(W-max X)`2 by A1,Th31;
A3: (W-min X)`1 = (W-max X)`1 by Th29;
  p`1 = (W-min X)`1 & (W-min X)`2 <= p`2 by A1,Th31;
  hence thesis by A3,A2,GOBOARD7:7;
end;
