intros. unfold abit in |- *. unfold elemlist in |- *.
apply (trunc_plus_petit bool) with (size - t).
unfold lt in H. inversion H. rewrite <- minus_Sn_m. auto with arith. auto with arith.
rewrite <- minus_Sn_m. auto with arith. apply le_Sn_le; auto with arith.
rewrite (strip_O bool). apply R1_lem. apply lt_le_weak. exact H.
Qed.
(****************************************************************)

(* Specifications: *)
Lemma lem_le_minus_v1_Sn :
forall n : nat,
S n <= size ->
n <= size ->
size - S n <= lengthbv (appbv (highs (R1 n)) (consbv (lowbit (R2 n)) nilbv)).