
theorem Th1:
  for p being FinSequence st len p <> 0 holds p|1 = <* p.1 *>
proof
  let p be FinSequence;
  assume len p <> 0;
  then A1: len(p|1) = 1 by NAT_1:14, FINSEQ_1:59;
  then 1 in dom(p|1) by FINSEQ_3:25;
  then A2: 1 in dom(p|Seg 1) by FINSEQ_1:def 16;
  (p|1).1 = (p|Seg 1).1 by FINSEQ_1:def 16
    .= p.1 by A2, FUNCT_1:47;
  hence thesis by A1, FINSEQ_1:40;
end;
