diff --git a/.obsidian/app.json b/.obsidian/app.json
index 6abe4c1..e69de29 100644
--- a/.obsidian/app.json
+++ b/.obsidian/app.json
@@ -1,3 +0,0 @@
-{
-  "alwaysUpdateLinks": true
-}
\ No newline at end of file
diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index f0739e3..01c65bd 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -51,8 +51,7 @@
               "title": "class 3"
             }
           }
-        ],
-        "currentTab": 1
+        ]
       }
     ],
     "direction": "vertical"
@@ -224,10 +223,10 @@
       "companion:Toggle completion": false
     }
   },
-  "active": "dd6c003f9d17b0e9",
+  "active": "6edd4157a160e462",
   "lastOpenFiles": [
-    "Concurrent Systems/slides/class 3.pdf",
     "Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md",
+    "Concurrent Systems/slides/class 3.pdf",
     "Concurrent Systems/notes/3a - Hardware primitives & Lamport Bakery algorithm.md",
     "Concurrent Systems/notes/1 - CS Basics.md",
     "Concurrent Systems/notes/2b - Round Robin algorithm.md",
diff --git a/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md b/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md
index 84952fb..53196e1 100644
--- a/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md	
+++ b/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md	
@@ -91,11 +91,11 @@ lock(i) :=
 	until foreach j != i, STAGE[j] = 0
 ```
 
--  $p_n$ invokes lock alone, completes its CS and its new DATE is n
-- all other $p_i, i \in P$ (with P being the set of all processes) will have `DATE[i] < n`, as their value for DATE is decreased
+-  $p_n$ invokes lock alone, completes its CS and so `DATE[n] = n`
+- then as DATE is either set to n or decreased, for each i, `DATE[i] < n`
 - *scenario 1*: every other $p_i$ keep invoking lock again immediately after the unlock
 	- every time some process exits the CS, `DATE[n]` is decreased
 	- after $n-1$ turns, `DATE[n]` will have `DATE[n] = 1`, with every other `DATE[i] > 1, i!=n`  -> ️✅
 - *scenario 2*: not every process invokes the lock
 	- eventually, more than one process will have its DATE set to 0
-	- but there will still be at most $n-1$ processes $p_i$ with `DATE[i] < DATE[n]`, this ensures that after $n-1$ -> ✅
\ No newline at end of file
+	- but there will still be at most $n-1$ processes $p_i$ with `DATE[i] < DATE[n]`, this ensures that after $n-1$ steps, every other process $p_i$ will have `DATE[i] > DATE[n]` -> ✅