reserve x,y,z,X for set,
  T for Universe;

theorem
  for T being non empty 1-sorted, N be net of T holds N is subnet of N
proof
  let T be non empty 1-sorted, N be net of T;
  take id N;
  thus the mapping of N = (the mapping of N)*id N by FUNCT_2:17;
  let m be Element of N;
  take n = m;
  let p be Element of N;
  assume n <= p;
  hence thesis;
end;
