#[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_morph_cons : forall P : list A -> Prop, (forall a l, P (l ++ [a]) -> P (a :: l)) -> Proper (@CPermutation A ==> iff) P.