Definition IndexSeq_NoDup b l: IndexSeq b l -> NoDup l.

(* Specifications: *)
Lemma IndexSeq_inv l: forall b, IndexSeq b l -> forall t, In t l -> b <= t < b + length l.
Lemma IndexSeq_base_lowest_value' (b: Index) l: IndexSeq b l -> forall e, In e l -> @Ele UE b e.
Lemma IndexSeq_cons (b: Index) l: IndexSeq (S b) l -> IndexSeq b (b :: l).
Lemma indices: exists tl, ol = map subscript tl /\ IndexSeq 0 tl.
Lemma IndexSeq_filterLt e n : forall b l, length l = n -> IndexSeq b l -> IndexSeq b (filter (fun f => unsum_bool (cmp_cmp (Ecmp UE f e) Lt)) l).
Lemma IndexSeq_filterGt e l: forall b, IndexSeq b l -> IndexSeq_above (b + length l) (filter (fun f => unsum_bool (cmp_cmp (Ecmp UE f e) Gt)) l).
Lemma InvIndexSeq_filterGt' e l b: IndexSeq b (e :: l) -> IndexSeq_above (b + S (length l)) (filter (fun f => unsum_bool (cmp_cmp (Ecmp UE f e) Gt)) l).