Section Sk.
Hypothesis k:nat.
Hypothesis Base_k: k<>0.
Inductive Base: (nat*(list nat))->Prop :=
| Base_intro s
(Base_a0':fst s = S O)
(Base_a:forall i, ai i s = if Nat.ltb i (k*2) then 2^(k*2-i) else O)
(Base_l:to_l s = k*2+1):
Base s.

Lemma Base_embanked {s1}:
Base s1 ->
exists s7 s_1 s_2,
embanked s1 s7 s_1 (2^(k*2)-1) s_2 (2^(k*2)) /\
(Add2 (k*2+1) s1 s7).