reserve A, B, X, Y for set;

theorem
  for N being non empty reflexive RelStr for x being Element of N, X
  being Subset of N st x in X holds uparrow x c= uparrow X
proof
  let N be non empty reflexive RelStr, x be Element of N, X be Subset of N
  such that
A1: x in X;
  let a be object;
  assume
A2: a in uparrow x;
  then reconsider b = a as Element of N;
  x <= b by A2,WAYBEL_0:18;
  hence thesis by A1,WAYBEL_0:def 16;
end;
