theorem Th54:
  for S, T, u st u in S^T holds S-head u in S & S-tail u in T
proof
  let S, T, u;
  assume u in S^T;
  then consider s, t such that A2: u = s^t & s in S & t in T by Def2;
  thus thesis by A2, Th52;
end;
