Lemma betweenf1 : forall(m:fmap)(u v u' v':dart), inv_hmap m -> exd m u' -> u <> u' -> v <> v' -> (betweenf m u' u v' /\ betweenf m u' v v') -> (betweenf m u u' v /\ betweenf m u v' v \/ betweenf m (cF m v) u' (cF_1 m u) /\ betweenf m (cF m v) v' (cF_1 m u)).