(* an induction principle for pairs of finite maps with equal support *)
Section FMapInd.
Variables (K : ordType) (V : Type).
Notation fmap := (finMap K V).
Notation nil := (@nil K V).

Lemma fmap_ind2 (P : fmap -> fmap -> Prop) :
P nil nil ->
(forall k v1 v2 s1 s2,
path ord k (supp s1) -> path ord k (supp s2) ->
P s1 s2 -> P (ins k v1 s1) (ins k v2 s2)) ->
forall s1 s2, supp s1 =i supp s2 -> P s1 s2.