diff --git a/cs3231/main.pdf b/cs3231/main.pdf
index 93b80f7..a963bbe 100644
Binary files a/cs3231/main.pdf and b/cs3231/main.pdf differ
diff --git a/cs3231/main.typ b/cs3231/main.typ
index 15b7236..bd32df1 100644
--- a/cs3231/main.typ
+++ b/cs3231/main.typ
@@ -30,3 +30,15 @@
   - $L_1 dot L_2 = L_1L_2 = {x y : x in L_1, y in L_2}$
   - $L^* = {x_1x_2...x_n : x_1, x_2, ... x_n in L, n in NN}$
   - $L^+ = {x_1x_2...x_n : x_1, x_2, ... x_n in L, n gt.eq 1}$
+
+=== Proof Structure
+==== Set A = Set B
+1. Show $A subset.eq B$
+  - Take *arbitrary* element $x in A$
+  - Use definition of A to show $x in B$
+  - Therefore, $A subset.eq B$
+2. Show $B subset.eq A$
+  - Take *arbitrary* element $x in B$
+  - Use definition of B to show $x in A$
+  - Therefore, $B subset.eq A$
+3. Since $A subset.eq B$ and $B subset.eq A$, $A = B$
diff --git a/cs4212/hw1-hellocaml-yadunut b/cs4212/hw1-hellocaml-yadunut
index a976b25..a152b7a 160000
--- a/cs4212/hw1-hellocaml-yadunut
+++ b/cs4212/hw1-hellocaml-yadunut
@@ -1 +1 @@
-Subproject commit a976b25ebb1434189ba15627bab1720fb345f518
+Subproject commit a152b7a34c9b2038b1588a3e28a5d156d41db0bf