(* TO BE A DOUBLE-LINK: *) 

Definition double_link(m:fmap)(x x':dart):Prop:=
  x <> x' /\ expe m x x'.

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.