(* Browse through the results of this query! *)

(** Which of the properties that you wrote down above have already
    been proved as theorems by the Coq library developers?  Answer
    here:

*)
(** [] *)

(** Let's use the permutation rules in the library to prove the
    following theorem. *)
    
Example butterfly: forall b u t e r f l y : nat,
  Permutation ([b;u;t;t;e;r]++[f;l;y]) ([f;l;u;t;t;e;r]++[b;y]).Example permut_example: forall (a b: list nat),
  Permutation (5::6::a++b) ((5::b)++(6::a++[])).Example not_a_permutation:
  ~ Permutation [1;1] [1;2].

Theorem maybe_swap_perm: forall al, Permutation al (maybe_swap al).