Section Append.
Variable (K : ordType) (V : Type).
Notation fmap := (finMap K V).
Notation nil := (nil K V).

(* backward induction principle *)
Lemma fmap_ind'' (P : fmap -> Prop) :
P nil -> (forall k v s, (forall x, x \in supp s -> ord x k) ->
P s -> P (ins k v s)) ->
forall s, P s.