
theorem Th12:
  for S being Circuit-like non void non empty ManySortedSign for
  A being non-empty Circuit of S, s being State of A for n being Nat holds
  Following(s,n+1) = Following Following(s,n)
proof
  let S be Circuit-like non void non empty ManySortedSign;
  let A be non-empty Circuit of S, s be State of A;
  let n be Nat;
  consider f being sequence of  product the Sorts of A such that
A1: Following(s,n) = f.n and
A2: f.0 = s and
A3: for n being Nat holds f.(n+1) = Following f.n by Def7;
  thus Following(s,n+1) = f.(n+1) by A2,A3,Def7
    .= Following Following(s,n) by A1,A3;
end;
