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 inf Y <= inf X
proof
  let X,Y be ext-real-membered set;
  assume
A1: X c= Y;
  inf Y is LowerBound of Y by Def4;
  then inf Y is LowerBound of X by A1,Th5;
  hence thesis by Def4;
end;
