intros H.
pose proof ndi as H0.
rewrite (Permutation.Permutation_sym (vec.List_Permutation (vec.remove_perm pi v))) in H0.
inversion_clear H0...
destruct (In_filter_inv _ _ _ H)...
Qed.

Lemma NoDup_comparisons (x: Index ee ol) (l: list (Index ee ol)):
NoDup (x :: l) -> NoDup (map (fun i: Index ee ol => U.unordered_nat_pair i x) l).