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 *)
(* um_filter *)

Lemma umfiltPt p k v :
um_filter p (pts k v : U) =
if p k then pts k v else if cond U k then Unit else um_undef.