proposition: Theorem rev_length_firsttry : forall l : natlist, length (rev l) = length l.
proof: Proof. intros l. induction l as [| n l' IHl']. - reflexivity. - simpl. rewrite <- IHl'. Abort. Theorem app_length : forall l1 l2 : natlist, length (l1 ++ l2) = (length l1) + (length l2). Proof. intros l1 l2. induction l1 as [| n l1' IHl1']. - reflexivity. - simpl. rewrite -> IHl1'. reflexivity. Qed.