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

theorem Th27:
  for T being non empty 1-sorted, N being net of T, J being
  net_set of the carrier of N, T, i being Element of N, f being Element of
product J, x being Element of Iterated J st x = [i,f] holds (Iterated J).x = (
  the mapping of J.i).(f.i)
proof
  let T be non empty 1-sorted, N be net of T, J be net_set of the carrier of N
, T, i be Element of N, f be Element of product J, x be Element of Iterated J;
  assume x = [i,f];
  hence (Iterated J).x = (the mapping of Iterated J).(i,f)
    .= (the mapping of J.i).(f.i) by Def13;
end;
