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Concurrent Systems/notes/9 - Consensus.md

@@ -130,11 +130,12 @@ Let pi invoke Z.op(par); to prove the Lemma, we need to show that eventually res
 It suffices to prove that ∃ k s.t. `CONS[k].propose(-)` returns a list that contains ⟨“op(par)”,i⟩ and pi participates to the consensus:
 1. since $p_i$ increases the sequence number of `LAST_OP[i]`,  eventually all the lists proposed contain that element forever
 2. eventually, $p_i$ will always find `invoc_i != ε` and participates with an increasing sequence number $k_i$
-3. let k be the first consensus where (a) holds
+3. let k be the first consensus where (1) holds
 4. by the properties of consensus, exec_i contains ⟨“op(par)”,i⟩
 
 As shown before, every invocation is executed; we have to show that this cannot happen more than once.
 
+**Lemma 2:** metti nome lemma
 If $p_i$ has inserted ⟨“op(par)”,sn⟩ in `LAST_OP[i]`, it cannot invoke another operation until ⟨“op(par)”,sn⟩ appears in a list chosen by the consensus
 - the sequence number of `LAST_OP[i]` can increase only after ⟨“op(par)”,sn⟩ has been executed