
theorem Th3:
  for S being non void Circuit-like non empty ManySortedSign for
  A being non-empty Circuit of S for s being State of A st s is stable
  for n being natural Number holds Following(s, n) = s
proof
  let S be non void Circuit-like non empty ManySortedSign;
  let A be non-empty Circuit of S;
  let s be State of A such that
A1: s is stable;
  let n be natural Number;
A0: n is Nat by TARSKI:1;
  defpred P[Nat] means Following(s,$1) = s;
A2: for n being Nat st P[n] holds P[n+1] by A1,FACIRC_1:12;
A3: P[ 0 ] by FACIRC_1:11;
  for n being Nat holds P[n] from NAT_1:sch 2(A3,A2);
  hence thesis by A0;
end;
