From 6e70f28ccbd5afc1506f71f013278a9d157ef03a Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 27 Oct 2022 20:40:09 +0200
Subject: Optimize last images, add proof template, improve CSS

---
 source/know/concept/dirac-delta-function/index.md | 20 ++++++--------------
 1 file changed, 6 insertions(+), 14 deletions(-)

(limited to 'source/know/concept/dirac-delta-function')

diff --git a/source/know/concept/dirac-delta-function/index.md b/source/know/concept/dirac-delta-function/index.md
index 518eba1..0185b78 100644
--- a/source/know/concept/dirac-delta-function/index.md
+++ b/source/know/concept/dirac-delta-function/index.md
@@ -65,11 +65,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-scale"/>
-<label for="proof-scale">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-scale">Proof.</label>
+
+{% include proof/start.html id="proof-scale" -%}
 Because it is symmetric, $$\delta(s x) = \delta(|s| x)$$.
 Then by substituting $$\sigma = |s| x$$:
 
@@ -77,9 +74,8 @@ $$\begin{aligned}
     \int \delta(|s| x) \dd{x}
     &= \frac{1}{|s|} \int \delta(\sigma) \dd{\sigma} = \frac{1}{|s|}
 \end{aligned}$$
+{% include proof/end.html id="proof-scale" %}
 
-</div>
-</div>
 
 An even more impressive property is the behaviour of the derivative of $$\delta(x)$$:
 
@@ -89,11 +85,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-dv1"/>
-<label for="proof-dv1">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-dv1">Proof.</label>
+
+{% include proof/start.html id="proof-dv1" -%}
 Note which variable is used for the
 differentiation, and that $$\delta'(x - \xi) = - \delta'(\xi - x)$$:
 
@@ -102,9 +95,8 @@ $$\begin{aligned}
     &= \dv{}{x}\int f(\xi) \: \delta(x - \xi) \dd{x}
     = f'(x)
 \end{aligned}$$
+{% include proof/end.html id="proof-dv1" %}
 
-</div>
-</div>
 
 This property also generalizes nicely for the higher-order derivatives:
 
-- 
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