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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">A</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<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>assume </b><a NAME="E1:8"/>
<font color="Maroon">O</font> <a href="relat_2.html#R6">is_connected_in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:8"/><b>then </b>
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">y</font> &amp; not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font> holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">y</font>,<font color="Olive">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><a class="ref" href="relat_2.html#D6">RELAT_2:def 6</a></i>;<br/>
<b>hence </b><a NAME="E3:8"/>
<font color="Maroon">O</font> <a href="relat_2.html#R6">is_connected_in</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="relat_2.html#D6">RELAT_2:def 6</a></i>;<br/>


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