<?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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">o</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arrow.html#K2" title="ARROW:func.2">LinPreorders</a> <font color="Maroon" title="c1">A</font> holds  <font color="Olive" title="b1">a</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Olive" title="b2">o</font>,<font color="Olive" title="b1">a</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">o</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arrow.html#K2" title="ARROW:func.2">LinPreorders</a> <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c2">a</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Olive" title="b1">o</font>,<font color="Maroon" title="c2">a</font></span><br/><b>let </b><font color="Maroon" title="c3">o</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arrow.html#K2" title="ARROW:func.2">LinPreorders</a> <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Maroon" title="c3">o</font>,<font color="Maroon" title="c2">a</font></span><br/>





<b>thus </b><a NAME="E1:12"/>
<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="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="c3">o</font>
 <b>by </b><i><a class="ref" href="arrow.html#D1" target="_self" title="ARROW:def.1">Def1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="arrow.html#D4" target="_self" title="ARROW:def.4">ARROW:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
