
theorem Th2:
  for p being FinSequence st len p <> 0
  holds p/^(len p -' 1) = <* p.len p *>
proof
  let p be FinSequence;
  assume len p <> 0;
  then A1: 1 <= len p by NAT_1:14;
  then A2: 1-1 <= len p - 1 by XREAL_1:9;
  A3: len p -' 1 <= len p by NAT_D:44;
  then A4: len(p/^(len p -' 1)) = len p - (len p + 0 -' 1) by RFINSEQ:def 1
    .= len p - (len p + 0 - 1) by A1, NAT_D:37
    .= 1;
  then 1 in dom(p/^(len p -' 1)) by FINSEQ_3:25;
  then (p/^(len p -' 1)).1 = p.(len p -' 1 + 1) by A3, RFINSEQ:def 1
    .= p.len p by A2, NAT_D:72;
  hence thesis by A4, FINSEQ_1:40;
end;
