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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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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#K9" title="FILTER_2:func.9">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">.&gt;</a></span> &amp; <font color="Olive" title="b1">IB</font> is  <a href="filter_2.html#V1" title="FILTER_2:attr.1">prime</a>  ) iff <font color="Olive" title="b1">IB</font> <a href="filter_2.html#R2" title="FILTER_2:pred.2">is_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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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#K9" title="FILTER_2:func.9">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">.&gt;</a></span> &amp; <font color="Maroon" title="c2">IB</font> is  <a href="filter_2.html#V1" title="FILTER_2:attr.1">prime</a>  ) iff <font color="Maroon" title="c2">IB</font> <a href="filter_2.html#R2" title="FILTER_2:pred.2">is_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#K7" title="FILTER_2:func.7">.:</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="E2:83"/>
<span class="p1"><a href="filter_2.html#K1" title="FILTER_2: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_2.html#K1" title="FILTER_2:func.1">.)</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_2.html#K9" title="FILTER_2:func.9">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">.&gt;</a></span>
 
;<br/>
<a NAME="E3:83"/><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#K9" title="FILTER_2:func.9">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">.&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#T58" title="FILTER_0:th.58">FILTER_0:58</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:83"/>
( ( <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#K9" title="FILTER_2:func.9">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K9" title="FILTER_2:func.9">.&gt;</a></span> &amp; <font color="Maroon" title="c2">IB</font> is  <a href="filter_2.html#V1" title="FILTER_2:attr.1">prime</a>  ) iff <font color="Maroon" title="c2">IB</font> <a href="filter_2.html#R2" title="FILTER_2:pred.2">is_max-ideal</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T33" target="_self" title="FILTER_2:th.33">Th33</a>, <a class="ref" href="filter_2.html#T44" target="_self" title="FILTER_2:th.44">Th44</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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