Axiom
  cut2_cons :
    forall (A : Elt) (v : Word), dans A X -> cut2 (cons A v) = cut2 v.

Lemma Deriveg_imp_Deriveg_cut : forall x y : Word, Deriveg X R x y -> ex2 (fun w : Word => Append (cut1 x) w = y) (fun w : Word => Deriveg X R (cut2 x) w).