intuition.
unfold RndNat.
eapply (well_formed_Repeat).
unfold eq_dec.
intuition.
eapply eq_nat_dec.
unfold RndNat_unchecked.
eapply well_formed_Bind.
eapply well_formed_Rnd.
intuition.
eapply well_formed_Ret.
eapply filter_In.
intuition.
2:{
unfold ltNatBool.
assert ((if (lt_dec O n) then true else false) = true).
destruct (lt_dec O n).
trivial.
omega.
eapply H0.
}
simpl.
eapply Fold.in_getUnique.
eapply Fold.in_flatten.
econstructor.
split.
eapply in_map_iff.
econstructor.
split.
eauto.
eapply in_getAllBvectors.
specialize (bvNat_zero (lognat n)); intuition.
simpl in *.
left.
eapply H0.
Qed.

Lemma RndNat_support_lt : forall n x,
In x (getSupport (RndNat n)) ->
x < n.