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

---
 .../concept/gronwall-bellman-inequality/index.md   | 33 ++++++++--------------
 1 file changed, 11 insertions(+), 22 deletions(-)

(limited to 'source/know/concept/gronwall-bellman-inequality')

diff --git a/source/know/concept/gronwall-bellman-inequality/index.md b/source/know/concept/gronwall-bellman-inequality/index.md
index 8096aaf..da1bcad 100644
--- a/source/know/concept/gronwall-bellman-inequality/index.md
+++ b/source/know/concept/gronwall-bellman-inequality/index.md
@@ -26,11 +26,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-original"/>
-<label for="proof-original">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-original">Proof.</label>
+
+{% include proof/start.html id="proof-original" -%}
 We define $$w(t)$$ to equal the upper bounds above
 on both $$w'(t)$$ and $$w(t)$$ itself:
 
@@ -63,8 +60,8 @@ $$\begin{aligned}
 
 Since $$u' \le \beta u$$ as a condition,
 the above derivative is always negative.
-</div>
-</div>
+{% include proof/end.html id="proof-original" %}
+
 
 Grönwall's inequality can be generalized to non-differentiable functions.
 Suppose we know:
@@ -84,11 +81,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-integral"/>
-<label for="proof-integral">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-integral">Proof.</label>
+
+{% include proof/start.html id="proof-integral" -%}
 We start by defining $$w(t)$$ as follows,
 which will act as shorthand:
 
@@ -138,8 +132,8 @@ $$\begin{aligned}
 \end{aligned}$$
 
 Insert this into the condition under which the Grönwall-Bellman inequality holds.
-</div>
-</div>
+{% include proof/end.html id="proof-integral" %}
+
 
 In the special case where $$\alpha(t)$$ is non-decreasing with $$t$$,
 the inequality reduces to:
@@ -151,11 +145,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-special"/>
-<label for="proof-special">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-special">Proof.</label>
+
+{% include proof/start.html id="proof-special" -%}
 Starting from the "ordinary" Grönwall-Bellman inequality,
 the fact that $$\alpha(t)$$ is non-decreasing tells us that
 $$\alpha(s) \le \alpha(t)$$ for all $$s \le t$$, so:
@@ -194,9 +185,7 @@ $$\begin{aligned}
     \\
     &\le \alpha(t) - \alpha(t) + \alpha(t) \exp\!\bigg( \int_0^t \beta(r) \dd{r} \bigg)
 \end{aligned}$$
-
-</div>
-</div>
+{% include proof/end.html id="proof-special" %}
 
 
 
-- 
cgit v1.2.3