theorem Th56:
  for S, s, t st s is S-headed holds
      s^t is S-headed & S-head (s^t) = S-head s & S-tail (s^t) = (S-tail s)^t
proof
  let S, s, t;
  assume s is S-headed;
  then consider q, r such that A1: q in S and A2: s = q^r;
  A3: s^t = q^(r^t) by A2, FINSEQ_1:32;
  hence s^t is S-headed by A1;
  thus S-head (s^t) = q by A1, A3, Th52 .= S-head s by A1, A2, Th52;
  thus S-tail (s^t) = r^t by A1, A3, Th52 .= (S-tail s)^t by A1, A2, Th52;
end;
