End Continuous.
Arguments cn_fresh [A][v][h][x] _.
(* Complete natmaps with binary range *)
Section Complete.
Variable A : Type.
Implicit Type h : natmap (A * A).
Definition complete v0 h vn :=
[/\ valid h, gapless h, continuous v0 h & last_val v0 h = vn].

Lemma cm_valid v0 h vn : complete v0 h vn -> valid h.