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

theorem Th8:
  for SCS being non-empty Circuit of IIG, v being Vertex of IIG,
      iv being InputValues of SCS holds
  IGTree(v,iv) = (Fix_inp_ext iv).v.IGTree(v,iv)
proof
  let SCS be non-empty Circuit of IIG, v be Vertex of IIG, iv be InputValues
  of SCS;
  reconsider igt = IGTree(v,iv) as Element of (the Sorts of FreeEnv SCS).v;
  ex e being Element of (the Sorts of FreeEnv SCS).v st card e = size(v,SCS
  ) & IGTree(v,iv) = (Fix_inp_ext iv).v.e by Def3;
  then card igt = size(v,SCS) by Th7;
  hence thesis by Def3;
end;
