diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index d2db11a..c1c26a8 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -34,9 +34,9 @@
               "type": "pdf",
               "state": {
                 "file": "Concurrent Systems/slides/class 6.pdf",
-                "page": 4,
+                "page": 5,
                 "left": -23,
-                "top": 143,
+                "top": 415,
                 "zoom": 0.6627078384798101
               },
               "icon": "lucide-file-text",
diff --git a/Concurrent Systems/notes/6 - Atomicity.md b/Concurrent Systems/notes/6 - Atomicity.md
index a2a7530..5616818 100644
--- a/Concurrent Systems/notes/6 - Atomicity.md	
+++ b/Concurrent Systems/notes/6 - Atomicity.md	
@@ -48,7 +48,8 @@ We now show that $\to$ is acyclic.
 		- Since $\hat{S}_X$ is a linearization of $\hat{H}|_X$ and op/op' are on X (literally because we have op ->x op'), this implies $res(op') <_X inv(op)$, which means that $op' \to_X op$, and so it won't be a total order... So this is not possible either.
 
 3. It cannot have cycles with more than 2 edges:
-	1. 
+	- by contradiction, consider a shortest cycle
+		- adjacent edges cannot belong to the same order (otw. the cycle would be shortable, because of transitivity)
 
 
 > [!PDF|red] class 6, p.6>  we would have a cycle of length