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2025-05-05 09:17:04 +02:00 · 2025-05-05 09:17:04 +02:00 · 65d4d02315
commit 65d4d02315
parent 4a03352005
2 changed files with 5 additions and 2 deletions
--- a/Systems/notes/15
+++ b/Systems/notes/15
@ -45,3 +45,7 @@ To simplify the proof, let us modify the set of formulae by allowing conjunction
 *Inductive step:* Let's assume the thesis for every tree of height at most h. Let h+1 be the height of $\phi$. Let's distinguish on the outmost operator in $\phi$
 ![](../../Pasted%20image%2020250505090603.png)
 ![](../../Pasted%20image%2020250505090959.png)
+
+(<=) We prove that $$R \triangleq \{ (P, Q) : L(P)=L(Q) \}$$ is a simulation; this suffices, since the relation just defined is trivially symmetric (so is a bisimulation too).
+
+Let $(P, Q) \in R$ and $$