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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#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:31"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">X</font> is <a href="waybel_6.html#V4">order-generating</a>
 ;<br/>

<b>let </b><font color="Maroon">x</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="E2:31"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="waybel16.html#K1" target="_self">Irr</a> <font color="Maroon">L</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E4:31"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K2">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">X</font></span>)</span>,<font color="Maroon">L</font>
 
<b>by </b><i>, <a class="ref" href="waybel_6.html#D5">WAYBEL_6:def 5</a></i>;<br/>
<a NAME="E5:31"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">x1</font> is <a href="waybel16.html#V1" target="_self">completely-irreducible</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:31"/>
 <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">X</font>,<font color="Maroon">L</font>
 
<b>by </b><i>, <a class="ref" href="waybel_6.html#D5">WAYBEL_6:def 5</a></i>;<br/>
<a NAME="E7:31"/><b>then </b>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">x1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="waybel16.html#T1" target="_self">Th1</a>, , </i>;<br/>
<b>hence </b><a NAME="E8:31"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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