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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>;<br/><b>let </b><font color="Maroon" title="c2">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>;<br/>



<b>assume </b><a NAME="E1:31"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c2">X</font> is <a href="waybel_6.html#V4" title="WAYBEL_6:attr.4">order-generating</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:31"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel16.html#K1" title="WAYBEL16:func.1">Irr</a> <font color="Maroon" title="c1">L</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">x1</font> = <font color="Maroon" title="c3">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<a NAME="E4:31"/><i><font color="Green" title="E20">A3</font></i>: 
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c4">x1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">X</font></span>)</span>,<font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="txt" href="waybel16.html#E1:31"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="waybel_6.html#D5" title="WAYBEL_6:def.5">WAYBEL_6:def 5</a></i>;<br/>
<a NAME="E5:31"/><i><font color="Green" title="E21">A4</font></i>: 
<font color="Maroon" title="c4">x1</font> is <a href="waybel16.html#V1" title="WAYBEL16:attr.1">completely-irreducible</a>
 
<b>by </b><i><a class="txt" href="waybel16.html#E2:31"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="waybel16.html#D4" target="_self" title="WAYBEL16:def.4">Def4</a></i>;<br/>
<a NAME="E6:31"/>
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c4">x1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="txt" href="waybel16.html#E1:31"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="waybel_6.html#D5" title="WAYBEL_6:def.5">WAYBEL_6:def 5</a></i>;<br/>
<a NAME="E7:31"/><b>then </b>
<font color="Maroon" title="c4">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c4">x1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="txt" href="waybel16.html#E4:31"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="waybel16.html#E5:31"><i><font color="Green" title="E21">A4</font></i></a>, <a class="ref" href="waybel16.html#T24" target="_self" title="WAYBEL16:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E8:31"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>


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