Definition inE := (mem_seq1, in_cons, inE).

(* Specifications: *)
Lemma has_nthP (a : pred T) s x0 : reflect (exists2 i, i < size s & a (nth x0 s i)) (has a s).
Lemma all_nthP (a : pred T) s x0 : reflect (forall i, i < size s -> a (nth x0 s i)) (all a s).
Lemma set_nth_default T s (y0 x0 : T) n : n < size s -> nth x0 s n = nth y0 s n.
Lemma headI T s (x : T) : rcons s x = head x s :: behead (rcons s x).