Definition remove_Znth {A} i (al : list A) := sublist 0 i al ++ sublist (i + 1) (Zlength al) al.

Lemma Zlength_remove_Znth : forall {A} i (l : list A), 0 <= i < Zlength l ->
Zlength (remove_Znth i l) = Zlength l - 1.