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

theorem Th51:
  for X being ext-real-membered set st -infty is UpperBound of X
  holds X c= {-infty}
proof
  let X be ext-real-membered set such that
A1: -infty is UpperBound of X;
  let x;
  assume x in X;
  then x = -infty by A1,Def1,XXREAL_0:6;
  hence thesis by TARSKI:def 1;
end;
