vault backup: 2025-04-30 19:43:22

Concurrent Systems/notes/14 Checking bisimilarity, an inference system.md

@@ -51,7 +51,7 @@ $P$ is in standard form if and only if $P \triangleq \sum_{i}\alpha_{i}P_{i}$ an
 	
 2. $P \triangleq \sum_{i \in I}\alpha_{i}P_{i}$. By induction $\forall P_{i} \exists P_{i}'$ in a standard form s.t. $\vdash P_{1}=P_{1}'$
 	Let's now consider a context: $\alpha_{1}.☐ + \sum_{i \in I}\alpha_{i}P_{i}$
-	Now we fill the context with $P_1$ and remove 1 from the set I (basically we pull it out from the summation): $$\alpha_{1}.P_{1} + \sum_{i \in I\setminus \{ 1 \}}\alpha_{i}P_{i}$$
+	Now we fill the hole (*er bucio*) with $P_1$ and remove 1 from the set I (basically we pull it out from the summation): $$\alpha_{1}.P_{1} + \sum_{i \in I\setminus \{ 1 \}}\alpha_{i}P_{i}$$
 	Now we replace $P_1$ with $P_{1}'$ and obtain: $$=\alpha_{1}.P_{1}' + \sum_{i \in I\setminus \{ 1 \}}\alpha_{i}P_{i}$$
 	imagine doing this until you pulled everything out... Standard form!