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```
% pandoc -f latex -t native
\newtheorem{theorem}{Theorem}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\theoremstyle{remark}
\newtheorem{remark}{Remark}
\begin{definition}[right-angled triangles] \label{def:tri}
A \emph{right-angled triangle} is a triangle whose sides of length~\(a\), \(b\) and~\(c\), in some permutation of order, satisfies \(a^2+b^2=c^2\).
\end{definition}
\begin{lemma}
The triangle with sides of length~\(3\), \(4\) and~\(5\) is right-angled.
\end{lemma}
\begin{proof}
This lemma follows from \cref{def:tri} since \(3^2+4^2=9+16=25=5^2\).
\end{proof}
\begin{theorem}[Pythagorean triplets] \label{thm:py}
Triangles with sides of length \(a=p^2-q^2\), \(b=2pq\) and \(c=p^2+q^2\) are right-angled triangles.
\end{theorem}
\begin{remark}
These are all pretty interesting facts.
\end{remark}
^D
[ Div
( "def:tri" , [ "definition" ] , [] )
[ Para
[ Strong [ Str "Definition 1" ]
, Str " (right-angled triangles). A "
, Emph [ Str "right-angled triangle" ]
, Str " is a triangle whose sides of length\160"
, Math InlineMath "a"
, Str ", "
, Math InlineMath "b"
, Str " and\160"
, Math InlineMath "c"
, Str ", in some permutation of order, satisfies "
, Math InlineMath "a^2+b^2=c^2"
, Str "."
]
]
, Div
( "" , [ "lemma" ] , [] )
[ Para
[ Strong [ Str "Lemma 2" ]
, Str ". "
, Emph
[ Str "The triangle with sides of length\160"
, Math InlineMath "3"
, Str ", "
, Math InlineMath "4"
, Str " and\160"
, Math InlineMath "5"
, Str " is right-angled."
]
]
]
, Div
( "" , [ "proof" ] , [] )
[ Para
[ Emph [ Str "Proof." ]
, Str " This lemma follows from "
, Link
( ""
, []
, [ ( "reference-type" , "ref" )
, ( "reference" , "def:tri" )
]
)
[ Str "Definition\160\&1" ]
( "#def:tri" , "" )
, Str " since "
, Math InlineMath "3^2+4^2=9+16=25=5^2"
, Str ".\160\9723"
]
]
, Div
( "thm:py" , [ "theorem" ] , [] )
[ Para
[ Strong [ Str "Theorem 3" ]
, Str " (Pythagorean triplets). "
, Emph
[ Str "Triangles with sides of length "
, Math InlineMath "a=p^2-q^2"
, Str ", "
, Math InlineMath "b=2pq"
, Str " and "
, Math InlineMath "c=p^2+q^2"
, Str " are right-angled triangles."
]
]
]
, Div
( "" , [ "remark" ] , [] )
[ Para
[ Emph [ Str "Remark 1" ]
, Str ". These are all pretty interesting facts."
]
]
]
```
|
