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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> ;<br/>

<b>assume </b><a NAME="E1:47_1_1"/>
not <font color="Maroon" title="c1">W</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c2">W</font> = <font color="Maroon" title="c1">W</font> as  non <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>consider </b><font color="Maroon" title="c3">w1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">W</font>;<br/>
<b>consider </b><font color="Maroon" title="c4">w2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">W</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="realset1.html#K5" title="REALSET1:func.5">{</a><span class="default"><font color="Maroon" title="c3">w1</font></span><a href="realset1.html#K5" title="REALSET1:func.5">}</a></span>;<br/>
<a NAME="E5:47_1_1"/>
( <font color="Maroon" title="c4">w2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">W</font> &amp; <font color="Maroon" title="c4">w2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">w1</font> &amp; ( <font color="Maroon" title="c3">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c3">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>  ) )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/>
<b>hence </b><a NAME="E6:47_1_1"/>
<font color="Maroon" title="c1">W</font> is <a href="setfam_1.html#V2" title="SETFAM_1:attr.2">with_non-empty_element</a>
 <b>by </b><i><a class="ref" href="setfam_1.html#D11" title="SETFAM_1:def.11">SETFAM_1:def 11</a></i>;<br/>


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