diff --git a/book/src/SUMMARY.md b/book/src/SUMMARY.md
index 930d34a..9265ae9 100644
--- a/book/src/SUMMARY.md
+++ b/book/src/SUMMARY.md
@@ -14,7 +14,7 @@
   - [Tips and tricks](user/tips-and-tricks.md)
 - [Design](design.md)
   - [Proving system](design/proving-system.md)
-    - [Lookup argument](design/proving-system/lookup-argument.md)
+    - [Lookup argument](design/proving-system/lookup.md)
     - [Permutation argument](design/proving-system/permutation.md)
     - [Circuit commitments](design/proving-system/circuit-commitments.md)
     - [Vanishing argument](design/proving-system/vanishing.md)
diff --git a/book/src/design/proving-system/circuit-commitments.md b/book/src/design/proving-system/circuit-commitments.md
index df2b390..d970e1f 100644
--- a/book/src/design/proving-system/circuit-commitments.md
+++ b/book/src/design/proving-system/circuit-commitments.md
@@ -41,7 +41,7 @@ follows:
   $$S_\text{compressed}(X) = \theta^{m-1} S_0(X) + \theta^{m-2} S_1(X) + \dots + \theta S_{m-2}(X) + S_{m-1}(X)$$
 
 - The prover then permutes $A_\text{compressed}(X)$ and $S_\text{compressed}(X)$ according
-  to the [rules of the lookup argument](lookup-argument.md), obtaining $A'(X)$ and $S'(X)$.
+  to the [rules of the lookup argument](lookup.md), obtaining $A'(X)$ and $S'(X)$.
 
 Finally, the prover creates blinding commitments for all of the lookups
 
diff --git a/book/src/design/proving-system/lookup-argument.md b/book/src/design/proving-system/lookup.md
similarity index 100%
rename from book/src/design/proving-system/lookup-argument.md
rename to book/src/design/proving-system/lookup.md