induction 1; intuition; simpl in *.
econstructor.
econstructor.
trivial.
econstructor.
trivial.
econstructor.
eapply H2.
eauto.
trivial.
trivial.
econstructor; trivial.
Qed.

(* Specifications: *)
Lemma repeat_low_tree_approx_same_inv
: forall (A : Set) (eqd : eq_dec A)(c : Comp A)(P : A -> bool) (n : nat) (a : A) (t : DistApproxTree A) (r : Rat),
well_formed_comp c ->
(exists a, In a (filter P (getSupport c))) ->
lowDistApprox_repeat c P a n r ->
dat_correct_repeat2 c P n t ->
n > 0 ->
r == lowDistApproxFromTree eqd t a.