Definition zeroI_e := compI zeroI nil nil.Definition leftI (d:nat)(x:TypeI) : nat :=
 match x with
 | I n _ => n
 | E _ => d
 end.

(* Specifications: *)
Lemma inf_list_maxl_l : forall l n s, inf_list l = I n s -> n = maxl (map (leftI 0) l).