End Translation.
Section Completeness.
(* Lemma reduce_poly_of_formula_simpl : forall fl fr var, simpl_eval (var_of_list var) (reduce (poly_of_formula fl)) = simpl_eval (var_of_list var) (reduce (poly_of_formula fr)) -> formula_eval var fl = formula_eval var fr.  (* Soundness of the method ; immediate *)

Lemma reduce_poly_of_formula_sound : forall fl fr var,
reduce (poly_of_formula fl) = reduce (poly_of_formula fr) ->
formula_eval var fl = formula_eval var fr.