reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;
reserve D for set,
  f for FinSequence of D;

theorem
  for D being set, f being FinSequence of D st
  k+1 <= len f holds f|(k+1) = f|k^<*f/.(k+1)*>
proof
  let D be set, f be FinSequence of D;
A1: 1 <= k+1 by NAT_1:12;
  assume k+1 <= len f;
  then
A2: k+1 in dom f by A1,FINSEQ_3:25;
  then f|Seg(k+1) = (f|k)^<*f.(k+1)*> by Th10 .= (f|k)^<*f/.(k+1)*>
    by A2,PARTFUN1:def 6;
  hence thesis;
end;
