(* VERY IMPORTANT: COROLLARIES: *)

(* Specifications: *)
Lemma not_exds_Iter_f_i :
forall(m:fmap)(z:dart)(i:nat),
let sr := Iter_rem m z in
let n := Iter_upb m z in
(i <= n)%nat -> ~ exds sr (Iter (f m) i z).
Lemma exds_Iter_f_i :
forall(m:fmap)(z:dart)(i:nat),
inv_hmap m -> exd m z ->
let s := Iter_orb m z in
let n := Iter_upb m z in
(i <= n)%nat -> exds s (Iter (f m) i z).