diff --git a/src/op/c-star/gns.tex b/src/op/c-star/gns.tex
index e850969..46c44a0 100644
--- a/src/op/c-star/gns.tex
+++ b/src/op/c-star/gns.tex
@@ -119,7 +119,7 @@
     then $\phi_1$ and $\phi_2$ are vector states on $A$. Since $M$ and $M^\perp$ are invariant for $\pi$, 
     \begin{align*}
         \dpn{x, \phi}{A} &= \dpn{\pi(x)\xi, \xi}{H} = \dpn{\pi(x)P\xi, P\xi}{H} + \dpn{\pi(x)(I - P)\xi, (I - P)\xi}{H} \\
-        &= \norm{P\xi}_H^2\dpn{\pi(x)\xi_1, \xi_1}{H} + \norm{(1 - P)\xi}_H^2 \dpn{\pi(x)\xi_2, \xi_2}{H} \\
+        &= \norm{P\xi}_H^2\dpn{\pi(x)\xi_1, \xi_1}{H} + \norm{(I - P)\xi}_H^2 \dpn{\pi(x)\xi_2, \xi_2}{H} \\
         &= \norm{P\xi}_H^2 \dpn{x, \phi_1}{A} + \norm{(I - P)\xi}_H^2 \dpn{x, \phi_2}{A}
     \end{align*}