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<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font> being <a href="waybel_7.html#V3" title="WAYBEL_7:attr.3">ultra</a> <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span><br/> for <font color="Olive" title="b2">M</font> being   <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of  <a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Olive" title="b1">F</font> holds   <a href="waybel33.html#K1" title="WAYBEL33:func.1">lim_inf</a> <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <font color="Olive" title="b2">M</font></span><br/><b>let </b><font color="Maroon" title="c2">F</font> be  <a href="waybel_7.html#V3" title="WAYBEL_7:attr.3">ultra</a> <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M</font> being   <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of  <a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font> holds   <a href="waybel33.html#K1" title="WAYBEL33:func.1">lim_inf</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <font color="Olive" title="b1">M</font></span><br/><b>let </b><font color="Maroon" title="c3">M</font> be    <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of  <a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel33.html#K1" title="WAYBEL33:func.1">lim_inf</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <font color="Maroon" title="c3">M</font></span><br/>





<a NAME="E1:30"/><i><font color="Green" title="E21">A1</font></i>: 
 <a href="waybel33.html#K1" title="WAYBEL33:func.1">lim_inf</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel33.html#T13" target="_self" title="WAYBEL33:th.13">Th13</a></i>;<br/>
<a NAME="E2:30"/>
for <font color="Olive" title="b1">p</font> being <a href="waybel28.html#V1" title="WAYBEL28:attr.1">greater_or_equal_to_id</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> holds   <a href="waybel33.html#K1" title="WAYBEL33:func.1">lim_inf</a> <font color="Maroon" title="c2">F</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a>  <a href="waybel_9.html#K2" title="WAYBEL_9:func.2">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Olive" title="b1">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel33.html#T15" target="_self" title="WAYBEL33:th.15">Th15</a></i>;<br/>
<b>hence </b><a NAME="E3:30"/>
 <a href="waybel33.html#K1" title="WAYBEL33:func.1">lim_inf</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <font color="Maroon" title="c3">M</font>
 <b>by </b><i><a class="txt" href="#E1:30"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="waybel28.html#T15" title="WAYBEL28:th.15">WAYBEL28:15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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