clear.
unfold cnf_tt, eval_cnf,eval_clause.
simpl. tauto.
Qed.

Lemma eval_cnf_and_opt : forall env x y, eval_cnf env (and_cnf_opt x y) <-> eval_cnf env (and_cnf x y).
Definition eval_opt_clause (env : Env) (cl: option clause) :=
match cl with
| None => True
| Some cl => eval_clause env cl
end.