(* OK: *)

(* Specifications: *)
Lemma succf_exd : forall (m:fmap)(x:dart),
inv_qhmap m -> succf m x -> exd m x.
Lemma F_nil : forall m:fmap,
inv_qhmap m -> F m nil = nil.
Lemma succf_exd_F : forall (m:fmap)(x:dart),
inv_qhmap m -> succf m x -> exd m (F m x).
Lemma not_exd_F_nil : forall (m:fmap)(x:dart),
inv_qhmap m -> ~exd m x -> F m x = nil.
Lemma not_exd_F_1_nil : forall (m:fmap)(x:dart),
inv_qhmap m -> ~exd m x -> F_1 m x = nil.
Lemma eqc_eqc_A_1_l : forall m:fmap, inv_qhmap m ->
forall (k:dim)(x y:dart),
eqc m x y -> pred m k x -> eqc m (A_1 m k x) y.
Lemma eqc_A_r_eqc : forall m:fmap, inv_qhmap m ->
forall (k:dim)(x y:dart),
succ m k y ->  eqc m x (A m k y) -> eqc m x y.
Lemma expf_A_1_l_eqc : forall m:fmap,
inv_qhmap m ->
forall (x y:dart)(k:dim),
expf m (A_1 m k x) y -> eqc m x y.