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<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">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">I</font> being   <a href="filter_2.html#M2" title="FILTER_2:mode.2">Ideal</a> of <font color="Maroon" title="c1">L</font>  st <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a> &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">I</font> holds <br/>( <font color="Olive" title="b1">I</font> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <span class="p1"><a href="filter_2.html#K17" title="FILTER_2:func.17">(.</a><span class="default"><font color="Maroon" title="c1">L</font></span><a href="filter_2.html#K17" title="FILTER_2:func.17">.&gt;</a></span> &amp; <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> )</span><br/><b>let </b><font color="Maroon" title="c2">I</font> be    <a href="filter_2.html#M2" title="FILTER_2:mode.2">Ideal</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a> &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">I</font> implies ( <font color="Maroon" title="c2">I</font> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <span class="p1"><a href="filter_2.html#K17" title="FILTER_2:func.17">(.</a><span class="default"><font color="Maroon" title="c1">L</font></span><a href="filter_2.html#K17" title="FILTER_2:func.17">.&gt;</a></span> &amp; <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> ) )</span><br/>



<a NAME="E1:63"/>
<span class="p1"><a href="filter_2.html#K19" title="FILTER_2:func.19">(.</a><span class="default"><font color="Maroon" title="c2">I</font></span><a href="filter_2.html#K19" title="FILTER_2:func.19">.&gt;</a></span> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <font color="Maroon" title="c2">I</font>
 
<b>by </b><i><a class="ref" href="filter_2.html#T38" target="_self" title="FILTER_2:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E2:63"/>
( <font color="Maroon" title="c1">L</font> is <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a> &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">I</font> implies ( <font color="Maroon" title="c2">I</font> <a href="filter_2.html#R1" title="FILTER_2:pred.1">=</a> <span class="p1"><a href="filter_2.html#K17" title="FILTER_2:func.17">(.</a><span class="default"><font color="Maroon" title="c1">L</font></span><a href="filter_2.html#K17" title="FILTER_2:func.17">.&gt;</a></span> &amp; <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> ) )
 <b>by </b><i><a class="ref" href="filter_2.html#T42" target="_self" title="FILTER_2:th.42">Th42</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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