(* 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 supp_eq_ins (s1 s2 : fmap) k1 k2 v1 v2 :
path ord k1 (supp s1) -> path ord k2 (supp s2) ->
supp (ins k1 v1 s1) =i supp (ins k2 v2 s2) ->
k1 = k2 /\ supp s1 =i supp s2.