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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being   <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <font color="Maroon" title="c1">L</font> holds   <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">L</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">F</font></span><br/><span class="kw">let </span><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>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">L</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">F</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">x</font> =  the    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">F</font>;<br/>
<a NAME="E1:52"/>
 <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">L</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a>  the    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T45" onmouseover="rs('yellow_0/T45')" onmouseout="rh()">YELLOW_0:45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:52"/>
 <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">L</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#D20" onmouseover="rs('waybel_0/D20')" onmouseout="rh()">WAYBEL_0:def 20</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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