reserve R for non empty RelStr,
  N for net of R,
  i for Element of N;

theorem Th42:
  for L being non empty RelStr, S being upper Subset of L,
  x being Element of L st x in S holds uparrow x c= S
proof
  let L be non empty RelStr, S be upper Subset of L, x be Element of L;
  assume
A1: x in S;
  let e be object;
  assume
A2: e in uparrow x;
  then reconsider y = e as Element of L;
  x <= y by A2,WAYBEL_0:18;
  hence thesis by A1,WAYBEL_0:def 20;
end;
