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

theorem
  for IIG for SCS being non-empty Circuit of IIG, s being State of SCS,
  v being Vertex of IIG holds s.v in (the Sorts of SCS).v
proof
  let IIG;
  let SCS be non-empty Circuit of IIG, s be State of SCS, v be Vertex of IIG;
  dom the Sorts of SCS = the carrier of IIG & ex g being Function st s = g
  & dom g = dom the Sorts of SCS &
  for x being object st x in dom the Sorts of SCS
  holds g.x in (the Sorts of SCS).x by CARD_3:def 5,PARTFUN1:def 2;
  hence thesis;
end;
