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

Lemma HT_upd_exists : forall H k v (HH : match H k with Some lv => exists v, value_of lv v | None => True end),
exists H', HT_upd H k v H'.