Definition tnth t i := nth (tnth_default t i) t i.

(* Specifications: *)
Lemma tnth_nth x t i : tnth t i = nth x t i.
Lemma eq_from_tnth t1 t2 : tnth t1 =1 tnth t2 -> t1 = t2.
Lemma tupleE t : tuple (fun sP => @Tuple t sP) = t.