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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is <a href="cohsp_1.html#V2" title="COHSP_1:attr.2">c=filtered</a> implies  not <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )</span><br/>

<b>consider </b><font color="Maroon" title="c2">Y</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>
<b>assume </b><a NAME="E2:13_2_1"/>
for <font color="Olive" title="b1">Y</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  ex <font color="Olive" title="b2">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( ( for <font color="Olive" title="b3">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> holds <br/><font color="Olive" title="b2">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">y</font> ) &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cohsp_1.html#D5" target="_self" title="COHSP_1:def.5">COHSP_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a></span><br/>

<a NAME="E3:13_2_1"/><b>then </b>
 ex <font color="Olive" title="b1">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( ( for <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> holds <br/><font color="Olive" title="b1">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">y</font> ) &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> )
 
;<br/>
<b>hence </b><a NAME="E4:13_2_1"/>
not <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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