theorem Th52:
  for S, s, t st s in S holds S-head (s^t) = s & S-tail (s^t) = t
proof
  let S, s, t;
  assume A1: s in S;
  set u = s^t;
  u is S-headed by A1;
  hence S-head u = s by A1, Def22;
  hence thesis by Def23;
end;
