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

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