(* Add n normal arguments and s safe argument at the beginnings *)
Definition BC_dummies (n n0 s s0 : nat)(e : BC) : BC :=
comp (n+n0) (s+s0) e (map (proj (n+n0) 0)      (seq n        n0))
(map (proj (n+n0) (s+s0)) (seq (n+n0+s) s0)).

(* Specifications: *)
Lemma dummies_inf : forall e n n0 s s0,
arities e = ok_arities n0 s0 ->
arities (BC_dummies n n0 s s0 e) = ok_arities (n + n0) (s + s0).
Lemma BC_dummies_correct : forall e n n0 s s0 nl sl,
length nl = n + n0 ->
length sl = s + s0 ->
sem (BC_dummies n n0 s s0 e) nl sl = sem e (skipn n nl) (skipn s sl).