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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="cardfil4.html#K1" title="CARDFIL4:func.1">[:</a><span class="default"><a href="cardfil2.html#K11" title="CARDFIL2:func.11">base_of_frechet_filter</a>,<a href="cardfil2.html#K11" title="CARDFIL2:func.11">base_of_frechet_filter</a></span><a href="cardfil4.html#K1" title="CARDFIL4:func.1">:]</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">  ex <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st  <a href="cardfil4.html#K4" title="CARDFIL4:func.4">square-uparrow</a> <font color="Olive" title="b1">n</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c1">x</font></span><br/>

<a NAME="E1:47"/>
 ex <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c1">x</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><span class="p2">(<span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Olive" title="b2">j</font></span>)</span></span>)</span></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cardfil4.html#T38" target="_self" onmouseover="rs('cardfil4/T38')" onmouseout="rh()">Th31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:47"/>
 ex <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st  <a href="cardfil4.html#K4" title="CARDFIL4:func.4">square-uparrow</a> <font color="Olive" title="b1">n</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cardfil4.html#T33" target="_self" onmouseover="rs('cardfil4/T33')" onmouseout="rh()">Th28</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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