(* forward induction on valid natmaps *)

(* Specifications: *)
Lemma valid_indf (P : natmap A -> Prop) :
P Unit ->
(forall t u h, P h ->
(forall x, x \in dom h -> t < x) ->
valid (t \-> u \+ h) -> P (t \-> u \+ h)) ->
forall h, valid h -> P h.