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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">IB</font> being   <a href="filter_2.html#M2" title="FILTER_2:mode.2">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#K17" title="FILTER_2:func.17">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K17" title="FILTER_2:func.17">.&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/><b>let </b><font color="Maroon" title="c2">IB</font> be    <a href="filter_2.html#M2" title="FILTER_2:mode.2">Ideal</a> of <font color="Maroon" title="c1">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#K17" title="FILTER_2:func.17">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K17" title="FILTER_2:func.17">.&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/>



<b>reconsider </b><font color="Maroon" title="c3">F</font> = <font color="Maroon" title="c2">IB</font> <a href="filter_2.html#K15" title="FILTER_2:func.15">.:</a>  as    <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c1">B</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  ;<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#K17" title="FILTER_2:func.17">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K17" title="FILTER_2:func.17">.&gt;</a></span>
 
;<br/>
<a NAME="E3:83"/><b>then </b>
( ( <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#K17" title="FILTER_2:func.17">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K17" title="FILTER_2:func.17">.&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> <a href="filter_0.html#NR1" title="FILTER_0:NR.1">is_ultrafilter</a>  )
 
<b>by </b><i><a class="ref" href="filter_0.html#T58" title="FILTER_0:th.58">FILTER_0:58</a></i>;<br/>
<b>hence </b><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#K17" title="FILTER_2:func.17">(.</a><span class="default"><font color="Maroon" title="c1">B</font></span><a href="filter_2.html#K17" title="FILTER_2:func.17">.&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>  )
 <b>by </b><i><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></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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