/usr/share/lyx/examples/xyfigure.lyx is in lyx-common 2.2.3-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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\lyxformat 508
\begin_document
\begin_header
\save_transient_properties true
\origin /systemlyxdir/examples/
\textclass article
\begin_preamble
\usepackage[all]{xy}
\end_preamble
\use_default_options false
\maintain_unincluded_children false
\language english
\language_package default
\inputencoding auto
\fontencoding global
\font_roman "default" "default"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry false
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 0
\use_package esint 0
\use_package mathdots 1
\use_package mathtools 0
\use_package mhchem 1
\use_package stackrel 0
\use_package stmaryrd 0
\use_package undertilde 0
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 0
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\quotes_language english
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header
\begin_body
\begin_layout Section*
Editing
\begin_inset ERT
status collapsed
\begin_layout Plain Layout
\backslash
Xy
\end_layout
\end_inset
-Pic figures in \SpecialChar LyX
\end_layout
\begin_layout Standard
Below you see an
\begin_inset ERT
status collapsed
\begin_layout Plain Layout
\backslash
Xy
\end_layout
\end_inset
-Pic diagram inside \SpecialChar LyX
being edited and to the right you see how the diagram
appears as soon as the cursor leaves the editing area.
\end_layout
\begin_layout Standard
\begin_inset Formula $\xymatrix{A\ar[d]\ar[r] & B\ar[d]\ar@{-->}[dl]\\
C\ar@{_{(}->}[r] & D\ar@/{}_{1pc}/[u]
}
$
\end_inset
\begin_inset Formula $\xymatrix{\, & \, & \mbox{}A\ar[r]\ar[d] & B\ar[d]\ar@{-->}[dl]\\
\, & & C\ar@{_{(}->}[r] & D\ar@/_{1pc}/[u]
}
$
\end_inset
\end_layout
\end_body
\end_document
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