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-rw-r--r--source/know/concept/impulse-response/index.md10
1 files changed, 3 insertions, 7 deletions
diff --git a/source/know/concept/impulse-response/index.md b/source/know/concept/impulse-response/index.md
index 397ac2d..661ed3f 100644
--- a/source/know/concept/impulse-response/index.md
+++ b/source/know/concept/impulse-response/index.md
@@ -30,11 +30,8 @@ $$\begin{aligned}
}
\end{aligned}$$
-<div class="accordion">
-<input type="checkbox" id="proof-main"/>
-<label for="proof-main">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-main">Proof.</label>
+
+{% include proof/start.html id="proof-theorem" -%}
Starting from the definition of $$u_p(t)$$,
we shift the argument by some constant $$\tau$$,
and multiply both sides by the constant $$f(\tau)$$:
@@ -60,9 +57,8 @@ $$\begin{aligned}
\hat{L} \int_0^\infty f(\tau) \: u_p(t - \tau) \dd{\tau}
&= (f * u_p)(t) = \hat{L}\{ u(t) \} = f(t)
\end{aligned}$$
+{% include proof/end.html id="proof-theorem" %}
-</div>
-</div>
This is useful for solving initial value problems,
because any initial condition can be satisfied