diff --git a/diagram_circle_lemma.tex b/diagram_circle_lemma.tex
index 5c33d4cd31917f816e0f537f85f31a08df641310..46790653efb03ac16d346e4bdb73bc0e7dea316f 100644
--- a/diagram_circle_lemma.tex
+++ b/diagram_circle_lemma.tex
@@ -37,13 +37,13 @@
     }
 
     % Legend
-    \draw (-1,0)+(-0.5,-1) rectangle +(2.2,1);
+    \draw (-1,0)+(-0.5,-1) rectangle +(2.6,1);
     \draw[fill,red]   (-1.1,0.5)  circle (0.09);
     \draw[fill,blue]  (-1.1,0)    +(-0.1,-0.1) rectangle +(0.1,0.1);
     \draw[fill,green] (-1.1,-0.5) +(-0.15,-0.1) -- +(0.15,-0.1) -- +(0,0.15);
     \draw[anchor=west] (-1,0.5)  node {$I$};
-    \draw[anchor=west] (-1,0)    node {$I_{\mathrm{in}(n-l,k)}$};
-    \draw[anchor=west] (-1,-0.5) node {$I_{\mathrm{out}(n-l,k)}$};
+    \draw[anchor=west] (-1,0)    node {$I\cap [{\color{gray}n}{-l},r]_0$};
+    \draw[anchor=west] (-1,-0.5) node {$I\setminus[{\color{gray}n}{-l},r]_0$};
 
 
     % Bigger circle
@@ -51,8 +51,8 @@
         \draw[-,dashed] ({\a*\step}:\r+1) -- ({(\a+1)*\step}:\r+1);
         %\draw ({\a*\step}:\r+1) circle (0.05);
     }
-    \draw ({-5*\step}:\r+1) +(0.2,-0.2) node {$n-l$};
-    \draw ({4*\step}:\r+1) +(0.2,0.2) node {$k$};
+    \draw ({-5*\step}:\r+1) +(0.2,-0.2) node {${\color{gray}n}{-l}$};
+    \draw ({4*\step}:\r+1) +(0.2,0.2) node {$r$};
 
 
     %
@@ -65,10 +65,13 @@
     \draw ({1*\step}:\r-0.3) node {$1$};
     % n/2
     \draw ({12*\step}:\r-0.3) node {$\frac{n}{2}$};
+    % n-1
+    \draw ({-1*\step}:\r-0.3) +(-0.4,0) node {${\color{gray}n}{-1}$};
     % i_*
     \draw[->] ({10*\step}:\r-1) -- ({10*\step}:\r-0.2);
     \draw ({10*\step}:\r-1) +(0.3,0) node {$i_*$};
-    % n-1
-    \draw ({-1*\step}:\r-0.3) +(-0.4,0) node {$n-1$};
+    % j
+    \draw[->] ({0*\step}:\r-1.3) -- ({0*\step}:\r-0.8);
+    \draw ({0*\step}:\r-1) +(-0.4,0) node {$j$};
 \end{tikzpicture}
 \end{document}
