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<b>consider </b><font color="Maroon" title="c2">S</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">cap-closed</a> <a href="prob_1.html#V1" title="PROB_1:attr.1">compl-closed</a> <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">X</font>;<br/>
<b>take </b>
<font color="Maroon" title="c2">S</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c2">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">S</font> is <a href="prob_1.html#V1" title="PROB_1:attr.1">compl-closed</a> &amp; <font color="Maroon" title="c2">S</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">cap-closed</a> )</span><br/>

<b>thus </b><a NAME="E2:23_1_1"/>
( not <font color="Maroon" title="c2">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">S</font> is <a href="prob_1.html#V1" title="PROB_1:attr.1">compl-closed</a> &amp; <font color="Maroon" title="c2">S</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">cap-closed</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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