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<span class="kw">take </span><font color="Maroon" title="c3">I</font> =  <a href="filter_2.html#K4" title="FILTER_2:func.4">.:</a> <span class="p1"><a href="filter_0.html#K3" title="FILTER_0: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#K3" title="FILTER_2:func.3">.:</a></span>)</span></span><a href="filter_0.html#K3" title="FILTER_0:func.3">.)</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> &amp; (  for <font color="Olive" title="b1">I</font> being   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">L</font>  st <font color="Maroon" title="c2">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">I</font> holds <br/><font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">I</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E1:49_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#D4" onmouseover="rs('filter_0/D4')" onmouseout="rh()">FILTER_0:def 4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="filter_2.html#NM1" title="FILTER_2:NM.1">Ideal</a> of <font color="Maroon" title="c1">L</font>  st <font color="Maroon" title="c2">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">I</font> holds <br/><font color="Maroon" title="c3">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">I</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> )</span><br/>

<a NAME="E2:49_1_1"/>
<font color="Maroon" title="c4">J</font> <a href="filter_2.html#K3" title="FILTER_2:func.3">.:</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">J</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E3:49_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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="filter_0.html#D4" onmouseover="rs('filter_0/D4')" onmouseout="rh()">FILTER_0:def 4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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