(* TO BE A DOUBLE-LINK: *) 

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

Lemma cA0_Br1:forall(m:fmap)(x x' z:dart), inv_hmap m -> double_link m x x' -> cA (Br1 m x x') zero z = if eq_dart_dec x z then cA m zero x' else if eq_dart_dec x' z then cA m zero x else cA m zero z.