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<b>let </b><font color="Maroon" title="c1">W</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"> ( not <font color="Maroon" title="c1">W</font> is <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> implies  not <font color="Maroon" title="c1">W</font> is <a href="setfam_1.html#V2" title="SETFAM_1:attr.2">empty-membered</a> )</span><br/>

<b>assume </b><a NAME="E1:70_1_1"/>
not <font color="Maroon" title="c1">W</font> is <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</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">W</font> is <a href="setfam_1.html#V2" title="SETFAM_1:attr.2">empty-membered</a></span><br/>

<b>then consider </b><font color="Maroon" title="c2">w1</font>, <font color="Maroon" title="c3">w2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:70_1_1"/><i><font color="Green" title="E19">W1</font></i>: 
( <font color="Maroon" title="c2">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> &amp; <font color="Maroon" title="c3">w2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> )
 <b>and </b><br/><a NAME="E4:70_1_1"/><i><font color="Green" title="E20">W2</font></i>: 
<font color="Maroon" title="c2">w1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">w2</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D10" title="ZFMISC_1:def.10">ZFMISC_1:def 10</a></i>;<br/>
<a NAME="E5:70_1_1"/>
( <font color="Maroon" title="c2">w1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c3">w2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="#E4:70_1_1"><i><font color="Green" title="E20">W2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:70_1_1"/>
not <font color="Maroon" title="c1">W</font> is <a href="setfam_1.html#V2" title="SETFAM_1:attr.2">empty-membered</a>
 <b>by </b><i><a class="txt" href="#E3:70_1_1"><i><font color="Green" title="E19">W1</font></i></a>, <a class="ref" href="setfam_1.html#D11" target="_self" title="SETFAM_1:def.11">Def11</a></i>; <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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