Ltac iff_ring :=
  match goal with
  | |- ?F 0  ?X <-> ?F 0  ?Y => replace X with Y by ring ; tauto
  end.

Lemma xnormalise_correct : forall env f, (make_conj (fun x => eval_nformula env x -> False) (xnormalise f)) <-> eval_nformula env f.