
theorem
  for S being non void Circuit-like non empty ManySortedSign for A
  being non-empty Circuit of S, s being State of A for x being set st s
  is_stable_at x for n being Nat holds Following(s,n) is_stable_at x
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;
  let x be set such that
A1: for n being Nat holds (Following(s,n)).x = s.x;
  let n, m be Nat;
  thus (Following(Following(s,n),m)).x = (Following(s,n+m)).x by Th13
    .= s.x by A1
    .= (Following(s,n)).x by A1;
end;
