(* Calls forward_if with the current precondition to which the provided conditions are added *)
(* QQQ TODO does this already exist? Add to library? *)
Ltac forward_if_diff add := match add with
| (PROPx ?P2 (LOCALx ?Q2 (SEPx ?R2))) => match goal with
  | |- semax ?Delta (PROPx ?P1 (LOCALx ?Q1 (SEPx ?R1))) _ _ =>
    let P3 := fresh "P3" in let Q3 := fresh "Q3" in let R3 := fresh "R3" in
    pose (P3 := P1 ++ P2); pose (Q3 := Q1 ++ Q2); pose (R3 := R1 ++ R2);
    simpl in P3, Q3, R3;
    forward_if (PROPx P3 (LOCALx Q3 (SEPx R3)));
    subst P3 Q3 R3
  end
end.

Lemma update_partially_expanded_key: forall k j j' v key_chars, (* TODO what's the value of v? *) j = j'+k-8 -> upd_Znth (j' + k) (map Vint (pow_fun GrowKeyByOne (Z.to_nat j) (key_bytes_to_key_words key_chars)) ++ repeat_op_table (60 - j) Vundef id) v = (map Vint (pow_fun GrowKeyByOne (Z.to_nat (j + 1)) (key_bytes_to_key_words key_chars)) ++ repeat_op_table (60 - (j + 1)) Vundef id).