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Concurrent Systems/notes/13 - CCS cose varie.md

@@ -13,7 +13,7 @@ This means that the implementation and the specification do coincide. To show th
 ![](../../Pasted%20image%2020250415082906.png)
 
 ## Restrictions
-**Proposition:** a.P\a ∼ 0
+**Proposition:** $a.P \textbackslash a ∼ 0$
 *Proof:*
 - S = {(a.P\a , 0)} is a bisimulation
 
@@ -21,6 +21,11 @@ Which challenges can (a.P)\a have?
 - a.P can only perform a (and become P)
 - however, because of restriction, a.P\a is stuck
 
- No challenge from a.P\a, nor from 0 à bisimilar!
+ No challenge from a.P\a, nor from 0 -> bisimilar!
 
-**Proposition:** 
+**Proposition:** $\bar{a}.P \textbackslash a ∼ 0$
+*Proof is similar.*
+
+## Idempotency of Sum
+**Proposition:** $α.P+α.P+M ∼ α.P+M$
+*Proof:*