(* IDEM, WITH cF, cF_1 / Br1: *)

(* Specifications: *)
Lemma cF_Br1: forall(m:fmap)(x x' z:dart),
inv_hmap m -> double_link m x x' ->
cF (Br1 m x x') z =
if eq_dart_dec (cA m zero x) z then cA_1 m one x'
else if eq_dart_dec (cA m zero x') z then cA_1 m one x
else cF m z.
Lemma cF_1_Br1:forall(m:fmap)(x x' z:dart),
inv_hmap m -> double_link m x x' ->
cF_1 (Br1 m x x') z =
if eq_dart_dec x (cA m one z) then cA m zero x'
else if eq_dart_dec x' (cA m one z) then cA m zero x
else cF_1 m z.
Lemma cF_1_Br1_bis:forall(m:fmap)(x x' z:dart),
inv_hmap m -> double_link m x x' ->
cF_1 (Br1 m x x') z =
if eq_dart_dec (cA_1 m one x) z then cA m zero x'
else if eq_dart_dec (cA_1 m one x') z then cA m zero x
else cF_1 m z.