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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