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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">V</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>, <font color="Maroon">S</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>, <font color="Maroon">T</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:32"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">S</font> <a href="yellow_4.html#R2">is_coarser_than</a> <font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E2:32"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">V</font> is <a href="waybel_0.html#V13">upper</a>
 <b>and </b><br/><a NAME="E3:32"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">T</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font>
 ;<br/>

<b>let </b><font color="Maroon">q</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E4:32"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">S1</font> = <font color="Maroon">S</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> ;<br/>
<b>reconsider </b><font color="Maroon">b</font> = <font color="Maroon">q</font> as    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S1</font> <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E8:32"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> &amp; <font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="ref" href="yellow_4.html#D2">YELLOW_4:def 2</a></i>;<br/>
<b>thus </b><a NAME="E9:32"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 <b>by </b><i><a class="txt" href="waybel12.html#E1"><i><font color="Green">Lemma18</font></i></a>, , , <a class="ref" href="waybel_0.html#D20">WAYBEL_0:def 20</a></i>;<br/>


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