reserve a, b, n for Nat,
  r for Real,
  f for FinSequence of REAL;
reserve p for Prime;

theorem
  f |^ 1 = f
proof
A1: for k being Nat st 1 <= k & k <= len (f|^1) holds (f|^1).k = f.k
  proof
    let k be Nat;
    assume 1 <= k & k <= len (f|^1);
    then k in dom (f|^1) by FINSEQ_3:25;
    hence (f|^1).k = f.k |^ 1 by Def1
      .= f.k;
  end;
  len (f|^1) = len f by Def1;
  hence thesis by A1;
end;
