intuition.
simpl.
rewrite (@sumList_exactly_one _ x).
rewrite eqbBvector_complete.
destruct (EqDec_dec bool_EqDec true true); intuition.
rewrite ratMult_1_r.
reflexivity.
eapply getAllBvectors_NoDup.
apply in_getAllBvectors.
intuition.
destruct (EqDec_dec bool_EqDec (eqbBvector x b) true); intuition.
apply eqbBvector_sound in e.
intuition.
eapply ratMult_0_r.
Qed.
Local Opaque evalDist.
Section FixedInRndList.
Variable A : Set.
Variable eta : nat.

Theorem FixedInRndList_prob :
forall (ls : list A)(x : Bvector eta),
(Pr[lsR <-$ compMap _ (fun _ => {0, 1}^eta) ls; ret (if (in_dec (EqDec_dec _) x lsR) then true else false)
] <= (length ls) / 2 ^ eta)%rat.