Ltac cnf_simpl :=
        repeat match goal with
               | |- context[and_cnf_opt cnf_ff _ ] => rewrite and_cnf_opt_cnf_ff
               | |- context[and_cnf_opt _ cnf_ff] => rewrite and_cnf_opt_cnf_ff_r
               | |- context[and_cnf_opt _ cnf_tt] => rewrite and_cnf_opt_cnf_tt
               | |- context[or_cnf_opt cnf_ff _] => rewrite or_cnf_opt_cnf_ff
               | |- context[or_cnf_opt _ cnf_ff] => rewrite or_cnf_opt_cnf_ff_r
               end.

Lemma rxcnf_xcnf : forall {TX : kind -> Type} {AF:Type} (k: kind) (f:TFormula TX AF k) pol, fst (rxcnf pol f) = xcnf pol f.