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<span class="kw">let </span><font color="Maroon" title="c1">B</font> be   <a href="lattices.html#NM8" title="LATTICES:NM.8">B_Lattice</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">IB</font> being   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">B</font> holds <br/> ( ( <font color="Olive" title="b1">IB</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> &amp; <font color="Olive" title="b1">IB</font> is  <a href="filter_2.html#V2" title="FILTER_2:attr.2">prime</a>  ) iff <font color="Olive" title="b1">IB</font> is  <a href="filter_2.html#V1" title="FILTER_2:attr.1">max-ideal</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">IB</font> be   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">B</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"> ( ( <font color="Maroon" title="c2">IB</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> &amp; <font color="Maroon" title="c2">IB</font> is  <a href="filter_2.html#V2" title="FILTER_2:attr.2">prime</a>  ) iff <font color="Maroon" title="c2">IB</font> is  <a href="filter_2.html#V1" title="FILTER_2:attr.1">max-ideal</a>  )</span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">F</font> = <font color="Maroon" title="c2">IB</font> <a href="filter_2.html#K3" title="FILTER_2:func.3">.:</a>  as   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a></span>)</span> ;<br/>
<a NAME="E2:76"/>
<span class="p1"><a href="filter_0.html#K1" title="FILTER_0:func.1">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">B</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a></span>)</span></span><a href="filter_0.html#K1" title="FILTER_0:func.1">.)</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span>
 
;<br/>
<a NAME="E3:76"/><span class="kw">then </span>
( ( <font color="Maroon" title="c3">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> &amp; <font color="Maroon" title="c3">F</font> is  <a href="filter_0.html#V2" title="FILTER_0:attr.2">prime</a>  ) iff <font color="Maroon" title="c3">F</font> is  <a href="filter_0.html#V1" title="FILTER_0:attr.1">being_ultrafilter</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T45" onmouseover="rs('filter_0/T45')" onmouseout="rh()">FILTER_0:45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:76"/>
( ( <font color="Maroon" title="c2">IB</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="filter_2.html#K5" title="FILTER_2:func.5">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K5" title="FILTER_2:func.5">.&gt;</a></span> &amp; <font color="Maroon" title="c2">IB</font> is  <a href="filter_2.html#V2" title="FILTER_2:attr.2">prime</a>  ) iff <font color="Maroon" title="c2">IB</font> is  <a href="filter_2.html#V1" title="FILTER_2:attr.1">max-ideal</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T32" target="_self" onmouseover="rs('filter_2/T32')" onmouseout="rh()">Th32</a>, <a class="ref" href="filter_2.html#T43" target="_self" onmouseover="rs('filter_2/T43')" onmouseout="rh()">Th43</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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