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

theorem
  for X being non empty ext-real-membered set, x being LowerBound of X
  st x in X holds x = inf X
proof
  let X be non empty ext-real-membered set, x be LowerBound of X;
  assume x in X;
  then for y being LowerBound of X holds y <= x by Def2;
  hence thesis by Def4;
end;
