reserve IIG for monotonic Circuit-like non void non empty ManySortedSign;

theorem Th7:
  for A being non-empty Circuit of IIG, iv being InputValues of A,
v being Vertex of IIG, e, e1 being Element of (the Sorts of FreeEnv A).v st e1
  = (Fix_inp_ext iv).v.e holds card e = card e1
proof
  let A be non-empty Circuit of IIG, iv be InputValues of A, v be Vertex of
  IIG, e, e1 be Element of (the Sorts of FreeEnv A).v;
  assume e1 = (Fix_inp_ext iv).v.e;
  then dom e = dom e1 by Th6;
  hence card e = card dom e1 by CARD_1:62
    .= card e1 by CARD_1:62;
end;
