intuition.
edestruct dat_exists_repeat2.
eauto.
eapply leRat_trans.
2:{
eapply eqRat_impl_leRat.
symmetry.
eapply (repeat_low_tree_approx_same_inv); eauto.
}
destruct H0.
edestruct dat_exists.
eapply well_formed_Repeat; eauto.
eapply comp_eq_dec; eauto.
eapply leRat_trans.
eapply eqRat_impl_leRat.
symmetry.
eapply low_tree_approx_same_inv.
eauto.
eauto.
apply lowDistApprox_dat_better_le.
eapply dat_repeat_better.
econstructor; eauto.
eapply dat_correct_repeat_same; eauto.
trivial.
Grab Existential Variables.
eapply comp_eq_dec; eauto.
Qed.

Lemma lowDistApprox_Rnd_lt : forall n1 n2 a r,
lowDistApprox (Rnd n1) a n2 r ->
n2 < n1 ->
r == 0.