Definition pred_conj_aux {T:Type} {n:nat} (pred : arity T (S n)) (m : nat) (cp : cartesianPower T (S m)) (cpwd : cartesianPower T n) : Prop.

(* Specifications: *)
Lemma pcaHdTl {T:Type} {n:nat} : forall (pred : arity T (S n)) m cp cpwd, pred_conj_aux pred (S m) cp cpwd = (app_1_n pred (headCP cp) cpwd /\ pred_conj_aux pred m (tailCP cp) cpwd).