diff --git a/ma1522/lec_08.tex b/ma1522/lec_08.tex
new file mode 100644
index 0000000..e69de29
diff --git a/ma1522/lec_09.tex b/ma1522/lec_09.tex
new file mode 100644
index 0000000..e69de29
diff --git a/ma1522/lec_10.tex b/ma1522/lec_10.tex
new file mode 100644
index 0000000..e69de29
diff --git a/ma1522/lec_11.tex b/ma1522/lec_11.tex
new file mode 100644
index 0000000..e69de29
diff --git a/ma1522/lec_12.tex b/ma1522/lec_12.tex
new file mode 100644
index 0000000..e69de29
diff --git a/ma1522/lec_13.tex b/ma1522/lec_13.tex
new file mode 100644
index 0000000..e69de29
diff --git a/ma1522/preamble.tex b/ma1522/preamble.tex
index 146e28e..1b3ed83 100644
--- a/ma1522/preamble.tex
+++ b/ma1522/preamble.tex
@@ -19,6 +19,10 @@
 \colorlet{LightRed}{Red!15}
 \colorlet{LightGreen}{Green!15}
 
+\let\implies\Rightarrow
+\let\impliedby\Leftarrow
+\let\iff\Leftrightarrow
+
 \newcommand{\HRule}[1]{\rule{\linewidth}{#1}}
 
 \declaretheoremstyle[name=Theorem,]{thmsty}