proposition: Lemma pathbdir_rewrite first x y z t l : pathbdir first ((x, y) :: (z, t) :: l) = ((((if first then x else y) =? z) && pathbdir false ((z, t) :: l)) || ((if first then x else y) =? t) && pathbdir true ((z, t) :: l))%bool.
proof: Proof. reflexivity. Qed.
imports: Arith List Permutation