End AtVal.
(* Continuous maps with binary range *)
Section Continuous.
Variable A : Type.
Implicit Type h : natmap (A * A).
Definition continuous v h :=
forall k x, find k.+1 h = Some x -> oapp snd v (find k h) = x.1.

(* Specifications: *)
Lemma cn_undef v : continuous v um_undef.
Lemma cn_sub v h x y k :
valid (k.+1 \-> (x, y) \+ h) -> continuous v (k.+1 \-> (x, y) \+ h) ->
oapp snd v (find k h) = x.