(* Why isn't this automatic? *)
Instance zero_ord_preorder : RelationClasses.PreOrder zero_ord.
Instance table_incl_preorder : RelationClasses.PreOrder table_incl.

Lemma table_incl_upd : forall T i k v, 0 <= i < Zlength T -> zero_ord (fst (Znth i T)) k ->
map_incl (snd (Znth i T)) v -> table_incl T (upd_Znth i T (k, v)).