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 *)

Lemma domUnPt k v f :
dom (f \+ pts k v) =i
[pred x | valid (f \+ pts k v) & (k == x) || (x \in dom f)].