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 reduce2ndCompose :
forall (c n m : nat) (v : Vector.t (naryFunc n) m) (n0 : naryFunc n)
(g : naryFunc (S (S m))),
extEqual n
(evalComposeFunc n _
(Vector.cons (naryFunc n) n0 _ (Vector.cons (naryFunc n) (evalConstFunc n c) _ v))
g)
(evalComposeFunc n _ (Vector.cons (naryFunc n) n0 _ v) (fun x : nat => g x c)).