vault backup: 2025-04-29 08:43:47

Concurrent Systems/notes/14.md

@@ -22,3 +22,10 @@ basically we can let the left or the right process evolve, leaving the other unc
 ![](../../Pasted%20image%2020250429083535.png)
 $P$ is in standard form if and only if $P \triangleq \sum_{i}\alpha_{i}P_{i}$ and $\forall_{i}P_{i}$ is in standard form.
 
+**Lemma:** $\forall P \exists P'$* in standard form such that $\vdash P = P'$
+*Proof:* by induction on the structure of P.
+
+**Base case:** $P \triangleq 0$. It suffices to consider $P' \triangleq 0$ and conclude reflexivity.
+**Inductive step:** we have to consider three cases.
+
+2. P $$