From a8929fe5518ed7961512bdf29c11a1284b8628b7 Mon Sep 17 00:00:00 2001
From: Marco Realacci <marco@marcorealacci.me>
Date: Mon, 14 Apr 2025 17:10:00 +0200
Subject: [PATCH] vault backup: 2025-04-14 17:10:00

---
 .obsidian/workspace.json                            |  4 ++--
 .../notes/12 - CCS (che non so cosa voglia dire).md | 13 ++++---------
 2 files changed, 6 insertions(+), 11 deletions(-)

diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index dc03cc2..f97a7e7 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -238,10 +238,10 @@
       "companion:Toggle completion": false
     }
   },
-  "active": "84845736e00d5c98",
+  "active": "2882ba3b76891dd0",
   "lastOpenFiles": [
-    "Concurrent Systems/slides/class 12.pdf",
     "Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md",
+    "Concurrent Systems/slides/class 12.pdf",
     "Pasted image 20250414164549.png",
     "Concurrent Systems/notes/images/Pasted image 20250414082824.png",
     "Concurrent Systems/notes/11 - LTSs and Bisimulation.md",
diff --git a/Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md b/Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md
index cb282b0..48f1efc 100644
--- a/Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md	
+++ b/Concurrent Systems/notes/12 - CCS (che non so cosa voglia dire).md	
@@ -130,18 +130,13 @@ $$A' \mid B \xrightarrow{\tau} A \mid B'$$
 
 ##### ▶️ Step 3: Transition from B'
 From the definition:
-- $BB' \triangleq \bar{c}.B$
-	- So: B′→cˉBB' \xrightarrow{\bar{c}} B
+- $B' \triangleq \bar{c}.B$
+	- So: $B' \xrightarrow{\bar{c}} B$
 
 Now use the **right parallel rule**:
-
-B′→cˉBA∣B′→cˉA∣B\frac{B' \xrightarrow{\bar{c}} B}{A \mid B' \xrightarrow{\bar{c}} A \mid B}
-
+$$\frac{B' \xrightarrow{\bar{c}} B}{A \mid B' \xrightarrow{\bar{c}} A \mid B}$$
 ✅ **Third transition:**
-
-A∣B′→cˉA∣BA \mid B' \xrightarrow{\bar{c}} A \mid B
-
----
+$$A \mid B' \xrightarrow{\bar{c}} A \mid B$$
 
 ## 🔄 Full Transition Path