Section Ignore_Params.
Fixpoint ignoreParams (n m : nat) (f : naryFunc n) {struct m} :
naryFunc (m + n) :=
match m return (naryFunc (m + n)) with
| O => f
| S x => fun _ => ignoreParams n x f
end.
Definition projectionListPR (n m : nat) (p : m <= n) : PrimRecs n m.
intros.
induction m as [| m Hrecm].
exact (PRnil n).
assert (m < n).
apply lt_S_n.
apply le_lt_n_Sm.
apply p.
apply (PRcons _ m (projFunc _ _ H)).
apply Hrecm.
apply le_S_n.
apply le_S.
apply p.
Defined.
Definition projectionList (n m : nat) (p : m <= n) :
Vector.t (naryFunc n) m := evalPrimRecs n m (projectionListPR n m p).
End Ignore_Params.

Lemma evalPrimRecParam :
forall (n c d : nat) (g : naryFunc (S n)) (h : naryFunc (S (S (S n)))),
extEqual _ (evalPrimRecFunc n (g d) (fun x y : nat => h x y d) c)
(evalPrimRecFunc (S n) g h c d).