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

theorem
  for X,Y being ext-real-membered set st X c= Y holds sup X <= sup Y
proof
  let X,Y be ext-real-membered set;
  assume
A1: X c= Y;
  sup Y is UpperBound of Y by Def3;
  then sup Y is UpperBound of X by A1,Th6;
  hence thesis by Def3;
end;
