#[global]
Instance CPermutation_Equivalence A : Equivalence (@CPermutation A) | 10 := {
  Equivalence_Reflexive := @CPermutation_refl A ;
  Equivalence_Symmetric := @CPermutation_sym A ;
  Equivalence_Transitive := @CPermutation_trans A }.Implicit Types a b : A.Implicit Types l : list A.

Lemma CPermutation_length_2_inv : forall a b l, CPermutation [a; b] l -> l = [a; b] \/ l = [b; a].