From b698d9868f34ba59e249d16c82cc84ca153df219 Mon Sep 17 00:00:00 2001
From: Marco Realacci <marco@marcorealacci.me>
Date: Tue, 29 Apr 2025 08:43:47 +0200
Subject: [PATCH] vault backup: 2025-04-29 08:43:47

---
 Concurrent Systems/notes/14.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Concurrent Systems/notes/14.md b/Concurrent Systems/notes/14.md
index fb8f173..9602daa 100644
--- a/Concurrent Systems/notes/14.md	
+++ b/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 $$
\ No newline at end of file