reserve x,y,z,r,s for ExtReal;
reserve A,B for ext-real-membered set;

theorem Th69:
  A c= [.inf A, sup A.]
proof
  let x be ExtReal;
  assume
A1: x in A;
  then
A2: x <= sup A by Th4;
  inf A <= x by A1,Th3;
  hence thesis by A2,XXREAL_1:1;
end;
