<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c4">o''</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="arrow.html#K3" title="ARROW:func.3">LinOrders</a> <font color="Maroon" title="c1">A</font>;<br/>







<a NAME="E1:15"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">o''</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">o''</font> implies <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="ref" href="arrow.html#D2" target="_self" title="ARROW:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E2:15"/>
( <font color="Maroon" title="c2">a</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Maroon" title="c4">o''</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c3">b</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Maroon" title="c4">o''</font>,<font color="Maroon" title="c2">a</font> implies <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="ref" href="arrow.html#D4" target="_self" title="ARROW:def.4">Def4</a></i>;<br/>


</div>
