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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">O</font> be   <a href="orders_1.html#NM2">Order</a> of <font color="Maroon">X</font>;<br/>



<b>thus </b><a NAME="E1:18"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">O</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:18_1"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">O</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:18_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E3:18_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:18_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">O</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D4">RELAT_1:def 4</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:18"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">O</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:18"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E4:18"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:18"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">O</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D5">RELAT_1:def 5</a></i>;<br/>


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