diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index c8ca628..a9bcaab 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -213,9 +213,10 @@
   },
   "active": "cdcc59f1bf6d4ae1",
   "lastOpenFiles": [
-    "Pasted image 20250505084556.png",
     "Concurrent Systems/slides/class 15.pdf",
     "Concurrent Systems/notes/15 - A formal language for LTSs.md",
+    "Pasted image 20250505084741.png",
+    "Pasted image 20250505084556.png",
     "Pasted image 20250505083948.png",
     "Pasted image 20250505083500.png",
     "Concurrent Systems/notes/14 Checking bisimilarity, an inference system.md",
@@ -235,8 +236,6 @@
     "Concurrent Systems/notes/images/Pasted image 20250415082906.png",
     "Concurrent Systems/slides/class 14.pdf",
     "Concurrent Systems/notes/images/Pasted image 20250429092543.png",
-    "Concurrent Systems/notes/images/Pasted image 20250429092305.png",
-    "Concurrent Systems/notes/images/Pasted image 20250429092055.png",
     "Concurrent Systems/slides/class 12.pdf",
     "HCIW/slides/HCI in the car.pdf",
     "Concurrent Systems/slides/class 11.pdf",
diff --git a/Concurrent Systems/notes/15 - A formal language for LTSs.md b/Concurrent Systems/notes/15 - A formal language for LTSs.md
index d712010..be6cb9e 100644
--- a/Concurrent Systems/notes/15 - A formal language for LTSs.md	
+++ b/Concurrent Systems/notes/15 - A formal language for LTSs.md	
@@ -21,4 +21,7 @@ where I is any indexing set (possibility, also infinite). Satisfiability for thi
 
 Of course, we can use the boolean constant FALSE (FF) and classical logical operators like disjunction $\lor$ and implication $=>$ (they can all be derived in the usual way from $TT, \lnot, \land$).
 
-Another very useful logical operator is "box": let us define $\lnot \lozenge a p$ 
\ No newline at end of file
+Another very useful logical operator is "box": let us define $\lnot \lozenge a p$ as $\square a \lnot \phi$
+![](../../Pasted%20image%2020250505084741.png)
+
+From the last condition, we have that $P $\models \square a \phi$ if and only if $$\forall P': P \xrightarrow{a} P' \implies P' \models \phi$$
diff --git a/Pasted image 20250505084741.png b/Pasted image 20250505084741.png
new file mode 100644
index 0000000..39df031
Binary files /dev/null and b/Pasted image 20250505084741.png differ