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We start by proving a lemma.
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We now prove a lemma that plays an important role in the proof of Theorem 3.3.
For this purpose we prove a lemma which establishes a Cauchy criterion for two sequences simultaneously.
Next we prove a lemma that provides a useful bound on B1 and λ1.
Next, we prove a lemma which will be used in the next section.
Next, we prove a lemma which will be useful in the development of the main theorems.
We need to prove a lemma before presenting our main theorem.
Now we prove a lemma, using similar steps to Theorem 1.2 in [16].
For convenience to prove the forward/backward secrecy for member joining/leaving, we first prove a lemma as follow.
To do so, we first introduce a definition and prove a lemma which will be useful to our main result.
First, we prove a lemma, which is the base for the proofs of the convergence rate in the ergodic sense.
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