auto.
Qed.
Hint Resolve double_zero.
Axiom
calcul4 :
forall a b c d : AV,
R (plus (plus a b) (plus c d)) (plus (plus a c) (plus b d)).

Lemma double_permute :
forall u v w t : V,
R (double (cons u v)) (double (cons w t)) ->
R (double (cons v u)) (double (cons t w)).