
theorem
  for L being RelStr, X, Y being Subset of L st X c= Y holds downarrow X
  c= downarrow Y
proof
  let L be RelStr, X, Y be Subset of L such that
A1: X c= Y;
  let q be object;
  assume
A2: q in downarrow X;
  then reconsider x = q as Element of L;
  ex z being Element of L st x <= z & z in X by A2,WAYBEL_0:def 15;
  hence thesis by A1,WAYBEL_0:def 15;
end;
