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<a NAME="E1:158_1_1"/>
<font color="Maroon">M</font> <a href="pboole.html#K6" target="_self">#</a>  is <a href="relat_1.html#V2">non-empty</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="158_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D16" target="_self">PBOOLE:def 16</a><br/>

<b>assume </b><a NAME="E1:158_1_1_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> <a href="finseq_2.html#K3">*</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">i</font> as    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">I</font> <a href="finseq_2.html#K3">*</a>  ;<br/>
<a NAME="E3:158_1_1_1"/>
not  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">M</font>
 
<b>by </b><i><a class="ref" href="pboole.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E4:158_1_1_1"/><b>then </b>
not  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#T25">FUNCT_1:25</a></i>;<br/>
<a NAME="E5:158_1_1_1"/><b>then </b>
 <a href="card_3.html#K4">product</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="card_3.html#T37">CARD_3:37</a></i>;<br/>
<b>hence </b><a NAME="E6:158_1_1_1"/>
not <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="pboole.html#K6" target="_self">#</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="pboole.html#T34" target="_self">Th34</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:158_1_1"/>
<font color="Maroon">M</font> <a href="pboole.html#K6" target="_self">#</a>  is <a href="relat_1.html#V2">non-empty</a>
 ;<br/>


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