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

theorem Th52:
  for X being ext-real-membered set st +infty is LowerBound of X
  holds X c= {+infty}
proof
  let X be ext-real-membered set such that
A1: +infty is LowerBound of X;
  let x;
  assume x in X;
  then x = +infty by A1,Def2,XXREAL_0:4;
  hence thesis by TARSKI:def 1;
end;
