1 files changed, 9 insertions, 15 deletions
diff --git a/source/know/concept/ito-integral/index.md b/source/know/concept/ito-integral/index.md
index f087f97..4a725e1 100644
--- a/source/know/concept/ito-integral/index.md
+++ b/source/know/concept/ito-integral/index.md
@@ -29,6 +29,7 @@ and $$\mathbf{E}[G_t^2]$$ is integrable for $$t \in [a, b]$$.
 If $$I_t$$ exists, $$G_t$$ is said to be **Itō-integrable** with respect to $$B_t$$.
 
 
+
 ## Motivation
 
 Consider the following simple first-order differential equation for $$X_t$$,
@@ -99,7 +100,8 @@ $$\begin{aligned}
 \end{aligned}$$
 
 For more information about applying the Itō integral in this way,
-see the [Itō calculus](/know/concept/ito-calculus/).
+see the [Itō calculus](/know/concept/ito-process/).
+
 
 
 ## Properties
@@ -138,11 +140,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-isometry"/>
-<label for="proof-isometry">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-isometry">Proof.</label>
+
+{% include proof/start.html id="proof-isometry" -%}
 We write out the left-hand side of the Itō isometry,
 where eventually $$h \to 0$$:
 
@@ -208,20 +207,16 @@ $$\begin{aligned}
     \longrightarrow
     \int_a^b \mathbf{E} \big[ G_t^2 \big] \dd{t}
 \end{aligned}$$
+{% include proof/end.html id="proof-isometry" %}
 
-</div>
-</div>
 
 Furthermore, Itō integrals are [martingales](/know/concept/martingale/),
 meaning that the average noise contribution is zero,
 which makes intuitive sense,
 since true white noise cannot be biased.
 
-<div class="accordion">
-<input type="checkbox" id="proof-martingale"/>
-<label for="proof-martingale">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-martingale">Proof.</label>
+
+{% include proof/start.html id="proof-martingale" -%}
 We will prove that an arbitrary Itō integral $$I_t$$ is a martingale.
 Using additivity, we know that the increment $$I_t \!-\! I_s$$
 is as follows, given information $$\mathcal{F}_s$$:
@@ -259,8 +254,7 @@ so from the Itō isometry we have $$\mathbf{E}[I]^2 < \infty$$,
 and therefore $$\mathbf{E}[I] < \infty$$,
 so $$I_t$$ has all the properties of a Martingale,
 since it is trivially $$\mathcal{F}_t$$-adapted.
-</div>
-</div>
+{% include proof/end.html id="proof-martingale" %}