Section UmpleqLemmas.
Variables (K : ordType) (A : Type) (U : union_map_class K A).
Implicit Types (x y a b : U) (p : pred K).
(* monotonicity lemmas *)
Hint Resolve umpleq_filtI : core.
(* x <= y and subdom *)
(* some/none lemmas *)

(* a weaker version of gen_domPtK, but legacy *)
Lemma domPt k v : dom (pts k v : U) =i [pred x | cond U k & k == x].