reserve x,y,z,r,s for ExtReal;

theorem Th2:
  y is LowerBound of {x} iff y <= x
proof
  x in {x} by TARSKI:def 1;
  hence y is LowerBound of {x} implies y <= x by Def2;
  assume
A1: y <= x;
  let z;
  assume z in {x};
  hence thesis by A1,TARSKI:def 1;
end;
