(*==========================================================
            TOPOLOGICAL HMAP OPERATIONS 
==========================================================*)

(* Empty hmap: *)

Definition v:= V.(* Insertion of an isolated dart, sewn to itself: *)

Definition prec_i (m:fmap)(x:dart):=
  prec_I m x.Definition i(m:fmap)(x:dart):=
  L (L (I m x) di0 x x) di1 x x.

Lemma inv_hmap_i: forall (m:fmap)(x:dart), inv_hmap m -> prec_i m x -> inv_hmap (i m x).