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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="lattices.html#NM1" title="LATTICES:NM.1">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">I</font>, <font color="Olive" title="b2">J</font> being  <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">I</font> <a href="filter_2.html#K12" title="FILTER_2:func.12">"\/"</a> <font color="Olive" title="b2">J</font> &amp; <font color="Olive" title="b2">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">I</font> <a href="filter_2.html#K12" title="FILTER_2:func.12">"\/"</a> <font color="Olive" title="b2">J</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font>, <font color="Maroon" title="c3">J</font> be   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">L</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">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font> <a href="filter_2.html#K12" title="FILTER_2:func.12">"\/"</a> <font color="Maroon" title="c3">J</font> &amp; <font color="Maroon" title="c3">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font> <a href="filter_2.html#K12" title="FILTER_2:func.12">"\/"</a> <font color="Maroon" title="c3">J</font> )</span><br/>





<a NAME="E1:74"/>
<font color="Maroon" title="c2">I</font> <a href="filter_2.html#K12" title="FILTER_2:func.12">"\/"</a> <font color="Maroon" title="c3">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">I</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a> </span>)</span> <a href="filter_0.html#K5" title="FILTER_0:func.5">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="filter_2.html#K7" title="FILTER_2:func.7">.:</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="filter_2.html#T45" target="_self" title="FILTER_2:th.45">Th45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:74"/>
( <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font> <a href="filter_2.html#K12" title="FILTER_2:func.12">"\/"</a> <font color="Maroon" title="c3">J</font> &amp; <font color="Maroon" title="c3">J</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font> <a href="filter_2.html#K12" title="FILTER_2:func.12">"\/"</a> <font color="Maroon" title="c3">J</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#T49" title="FILTER_0:th.49">FILTER_0:49</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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