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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM6" title="WAYBEL_0:NM.6">Semilattice</a>;<br/><b>let </b><font color="Maroon" title="c2">F</font> be   <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <font color="Maroon" title="c1">L</font>;<br/><b>let </b><font color="Maroon" title="c3">G</font> be    <a href="waybel12.html#M1" title="WAYBEL12:mode.1">GeneratorSet</a> of <font color="Maroon" title="c2">F</font>;<br/><b>let </b><font color="Maroon" title="c4">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <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="E1:49"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c3">G</font> <a href="yellow_4.html#R4" title="YELLOW_4:pred.4">is_coarser_than</a> <font color="Maroon" title="c4">A</font>
 ;<br/>

<b>assume </b><a NAME="E2:49"/>
<font color="Maroon" title="c4">A</font> <a href="yellow_4.html#R4" title="YELLOW_4:pred.4">is_coarser_than</a> <font color="Maroon" title="c2">F</font>
 ;<br/>

<a NAME="E3:49"/><b>then </b><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c4">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font>
 
<b>by </b><i><a class="ref" href="yellow_4.html#T8" title="YELLOW_4:th.8">YELLOW_4:8</a></i>;<br/>
<a NAME="E4:49"/>
<font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K12" title="WAYBEL_0:func.12">fininfs</a> <font color="Maroon" title="c3">G</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel12.html#D3" target="_self" title="WAYBEL12:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E5:49"/>
<font color="Maroon" title="c2">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K12" title="WAYBEL_0:func.12">fininfs</a> <font color="Maroon" title="c4">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel12.html#E1:49"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="waybel12.html#T8" target="_self" title="WAYBEL12:th.8">Th8</a>, <a class="ref" href="waybel12.html#T33" target="_self" title="WAYBEL12:th.33">Th33</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a>,<a class="ref" href="waybel12.html#D3" target="_self" title="WAYBEL12:def.3">WAYBEL12:def 3</a><br/>

<b>thus </b><a NAME="E6:49"/>
 <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K12" title="WAYBEL_0:func.12">fininfs</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font>
 <b>by </b><i><a class="txt" href="waybel12.html#E3:49"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="waybel_0.html#T62" title="WAYBEL_0:th.62">WAYBEL_0:62</a></i>;<br/>


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