
theorem
  for P being with_infima Poset, x, y being Element of P holds (waybelow
  x)"/\"(waybelow y) c= downarrow (x"/\"y)
proof
  let R be with_infima Poset, x, y be Element of R;
  {x}"/\"{y} = {x"/\"y} & (downarrow x)"/\"(downarrow y) c= downarrow ((
  downarrow x)"/\"(downarrow y)) by WAYBEL_0:16,YELLOW_4:46;
  then
A1: (downarrow x)"/\"(downarrow y) c= downarrow (x"/\"y) by YELLOW_4:62;
  waybelow x c= downarrow x & waybelow y c= downarrow y by WAYBEL_3:11;
  then (waybelow x)"/\"(waybelow y) c= (downarrow x)"/\"(downarrow y) by
YELLOW_4:48;
  hence thesis by A1;
end;
