Definition lel (l m:list A) := length l <= length m.

(* Specifications: *)
Lemma lel_refl : lel l l.
Lemma lel_trans : lel l m -> lel m n -> lel l n.
Lemma lel_cons_cons : lel l m -> lel (a :: l) (b :: m).
Lemma lel_cons : lel l m -> lel l (b :: m).
Lemma lel_tail : lel (a :: l) (b :: m) -> lel l m.
Lemma lel_nil : forall l':list A, lel l' [] -> [] = l'.