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<b>take </b><font color="Maroon" title="c3">I</font> =  <a href="filter_2.html#K14" title="FILTER_2:func.14">.:</a> <span class="p1"><a href="filter_2.html#K3" title="FILTER_2:func.3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">D</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a> </span>)</span></span><a href="filter_2.html#K3" title="FILTER_2:func.3">.)</a></span>;<br/>

<a NAME="E1:55_1_1"/><i><font color="Green" title="E20">A1</font></i>: 
( <font color="Maroon" title="c2">D</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D</font> &amp; <font color="Maroon" title="c3">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="filter_2.html#K3" title="FILTER_2:func.3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">D</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a> </span>)</span></span><a href="filter_2.html#K3" title="FILTER_2:func.3">.)</a></span> &amp; <font color="Maroon" title="c2">D</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="filter_2.html#K3" title="FILTER_2:func.3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">D</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a> </span>)</span></span><a href="filter_2.html#K3" title="FILTER_2:func.3">.)</a></span> &amp; ( for <font color="Olive" title="b1">F</font> being   <a href="filter_2.html#M1" title="FILTER_2:mode.1">Filter</a> of <font color="Maroon" title="c1">L</font> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>   st <font color="Maroon" title="c2">D</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> holds <br/><span class="p1"><a href="filter_2.html#K3" title="FILTER_2:func.3">&lt;.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">D</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a> </span>)</span></span><a href="filter_2.html#K3" title="FILTER_2:func.3">.)</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">F</font> ) )
 
<b>by </b><i><a class="ref" href="filter_0.html#D5" title="FILTER_0:def.5">FILTER_0:def 5</a></i>;<br/>
<b>hence </b><a NAME="E2:55_1_1"/>
<font color="Maroon" title="c2">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">I</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">J</font> be    <a href="filter_2.html#M2" title="FILTER_2:mode.2">Ideal</a> of <font color="Maroon" title="c1">L</font>;<br/>

<a NAME="E3:55_1_1"/>
<font color="Maroon" title="c4">J</font> <a href="filter_2.html#K15" title="FILTER_2:func.15">.:</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">J</font>
 
;<br/>
<b>hence </b><a NAME="E4:55_1_1"/>
( <font color="Maroon" title="c2">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">J</font> implies <font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">J</font> )
 <b>by </b><i><a class="txt" href="filter_2.html#E1:55_1_1"><i><font color="Green" title="E20">A1</font></i></a></i>;<br/>


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