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 downarrow x c= downarrow 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 downarrow x;
  then reconsider b = a as Element of N;
  b <= x by A2,WAYBEL_0:17;
  hence thesis by A1,WAYBEL_0:def 15;
end;
