
theorem Th4:
  for S being non void Circuit-like non empty ManySortedSign for
  A being non-empty Circuit of S for s being State of A,
  n1, n2 being natural Number st Following(s, n1) is stable & n1 <= n2
  holds Following(s, n2) = Following(s, n1)
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, n1, n2 be natural Number such that
A1: Following(s, n1) is stable and
A2: n1 <= n2;
  consider k being Nat such that
A3: n2 = n1+k by A2,NAT_1:10;
  reconsider k as Nat;
  n1 is Nat & n2 is Nat by TARSKI:1;
  then Following(s, n2) = Following(Following(s, n1), k) by A3,FACIRC_1:13;
  hence thesis by A1,Th3;
end;
