(* x <= y and subdom *)

(* Specifications: *)
Lemma umpleq_subdom x y : valid y -> [pcm x <= y] -> {subset dom x <= dom y}.
(* meet is the greatest lower bound *)
Lemma umpleq_meet a x y1 y2 :
valid (x \+ y1 \+ y2) ->
[pcm a <= x \+ y1] -> [pcm a <= x \+ y2] -> [pcm a <= x].