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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>  st <font color="Olive" title="b1">IB</font> <a href="filter_2.html#R2" title="FILTER_2:pred.2">is_max-ideal</a>  holds <br/>for <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font> holds <br/> ( <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">IB</font> iff not <font color="Olive" title="b2">a</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">IB</font> )</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="filter_2.html#R2" title="FILTER_2:pred.2">is_max-ideal</a>  implies for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font> holds <br/> ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">IB</font> iff not <font color="Olive" title="b1">a</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">IB</font> ) )</span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">FB</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/>
<span class="kw">assume </span><a NAME="E2:84"/>
<font color="Maroon" title="c2">IB</font> <a href="filter_2.html#R2" title="FILTER_2:pred.2">is_max-ideal</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">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">B</font> holds <br/> ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">IB</font> iff not <font color="Olive" title="b1">a</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">IB</font> )</span><br/>

<a NAME="E3:84"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<font color="Maroon" title="c3">FB</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_2.html#T33" target="_self" title="FILTER_2:th.33">Th33</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">IB</font> iff not <font color="Maroon" title="c4">a</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">IB</font> )</span><br/>

<a NAME="E4:84"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="filter_2.html#K5" title="FILTER_2:func.5">.:</a> </span>)</span> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="filter_2.html#E71"><span class="lab"><font color="Green" title="E27">Lm3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:84"/>
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">IB</font> iff not <font color="Maroon" title="c4">a</font> <a href="lattices.html#K7" title="LATTICES:func.7">`</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">IB</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="filter_0.html#T59" title="FILTER_0:th.59">FILTER_0:59</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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