Definition cnf_normalise {T: Type} (t: Formula C) (tg: T) : cnf NFormula T :=
let f := normalise t in
if check_inconsistent f then cnf_ff _ _
else cnf_of_list (xnormalise f) tg.
Definition cnf_negate {T: Type} (t: Formula C) (tg: T) : cnf NFormula T :=
let f := normalise t in
if check_inconsistent f then cnf_tt _ _
else cnf_of_list (xnegate f) tg.

Lemma eq0_cnf : forall x,
(0 < x -> False) /\ (0 < - x -> False) <-> x == 0.