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_impl_xcnf : forall {TX : kind -> Type} {AF:Type} (k: kind) (f1 f2:TFormula TX AF k) (IHf1 : forall pol : bool, fst (rxcnf pol f1) = xcnf pol f1) (IHf2 : forall pol : bool, fst (rxcnf pol f2) = xcnf pol f2), forall pol : bool, fst (rxcnf_impl rxcnf pol f1 f2) = mk_impl xcnf pol f1 f2.