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 p be FinSequence for n be Nat st 1 <= n & n <= len p holds
    p = (p|(n-'1))^<*p.n*>^(p/^n)
proof
  let p be FinSequence;
  let n be Nat;
  assume that
A1: 1 <= n and
A2: n <= len p;
  len p >= n-'1+1 by A1,A2,XREAL_1:235;
  then
A3: len p > n-'1 by NAT_1:13;
  p|n = p|(n-'1+1) by A1,XREAL_1:235
    .= p|(n-'1)^<*p.(n-'1+1)*> by A3,Th83
    .= p|(n-'1)^<*p.n*> by A1,XREAL_1:235;
  hence thesis by RFINSEQ:8;
end;
