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<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>, <font color="Maroon" title="c4">c</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="c5">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>;<br/>









<b>assume </b><a NAME="E1:14"/>
( <font color="Maroon" title="c2">a</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c3">b</font> or <font color="Maroon" title="c2">a</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c3">b</font> )
 ;<br/>

<a NAME="E2:14"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="arrow.html#T4" target="_self" title="ARROW:th.4">Th4</a></i>;<br/>
<a NAME="E3:14"/><b>then </b><i><font color="Green" title="E10">A1</font></i>: 
<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="c5">o</font>
 
<b>by </b><i><a class="ref" href="arrow.html#D4" target="_self" title="ARROW:def.4">Def4</a></i>;<br/>
<b>assume </b><a NAME="E4:14"/>
( <font color="Maroon" title="c3">b</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c4">c</font> or <font color="Maroon" title="c3">b</font> <a href="arrow.html#NR3" title="ARROW:NR.3">&lt;_</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c4">c</font> )
 ;<br/>

<a NAME="E5:14"/><b>then </b>
<font color="Maroon" title="c3">b</font> <a href="arrow.html#R1" title="ARROW:pred.1">&lt;=_</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="ref" href="arrow.html#T4" target="_self" title="ARROW:th.4">Th4</a></i>;<br/>
<a NAME="E6:14"/><b>then </b>
<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="c4">c</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="c5">o</font>
 
<b>by </b><i><a class="ref" href="arrow.html#D4" target="_self" title="ARROW:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E7:14"/>
<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="c4">c</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="c5">o</font>
 <b>by </b><i><a class="txt" href="arrow.html#E3:14"><i><font color="Green" title="E10">A1</font></i></a>, <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><br/>


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