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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">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>thus </b><a NAME="E1:100"/>
( ( <font color="Maroon">X</font> <a href="xboole_0.html#R2">c&lt;</a> <font color="Maroon">Y</font> or <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> or <font color="Maroon">Y</font> <a href="xboole_0.html#R2">c&lt;</a> <font color="Maroon">X</font> ) implies <font color="Maroon">X</font>,<font color="Maroon">Y</font> <a href="xboole_0.html#R3">are_c=-comparable</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="100_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:100_1"/>
( <font color="Maroon">X</font> <a href="xboole_0.html#R2">c&lt;</a> <font color="Maroon">Y</font> or <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> or <font color="Maroon">Y</font> <a href="xboole_0.html#R2">c&lt;</a> <font color="Maroon">X</font> )
 ;<br/>

<b>hence </b><a NAME="E2:100_1"/>
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> or <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D9">XBOOLE_0:def 9</a><br/>


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

<b>assume </b><a NAME="E2:100"/>
( <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> or <font color="Maroon">Y</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#D9">XBOOLE_0:def 9</a><br/>

<b>hence </b><a NAME="E3:100"/>
( <font color="Maroon">X</font> <a href="xboole_0.html#R2">c&lt;</a> <font color="Maroon">Y</font> or <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> or <font color="Maroon">Y</font> <a href="xboole_0.html#R2">c&lt;</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/>


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