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 freeUnPt2 k1 k2 v f :
valid (f \+ pts k2 v) ->
free k1 (f \+ pts k2 v) =
if k1 == k2 then f else free k1 f \+ pts k2 v.