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<b>let </b><font color="Maroon">p</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">P</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:26"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">P</font> = <font color="Maroon">P</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<a NAME="E3:26"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K3" target="_self">{$}</a> <font color="Maroon">P</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:26"/><b>then </b>
<span class="p1">(<span class="default"><a href="pnproc_1.html#K3" target="_self">{$}</a> <font color="Maroon">P</font></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="pnproc_1.html#K3" target="_self">{$}</a> <font color="Maroon">P</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E5:26"/><b>then </b>
<span class="p1">(<span class="default"><a href="pnproc_1.html#K3" target="_self">{$}</a> <font color="Maroon">P</font></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="funcop_1.html#K2">--&gt;</a> 0</span>)</span>
 
;<br/>
<a NAME="E6:26"/><b>then </b>
<span class="p1">(<span class="default"><a href="pnproc_1.html#K3" target="_self">{$}</a> <font color="Maroon">P</font></span>)</span> <a href="pnproc_1.html#K2" target="_self">.</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default">0</span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14">FUNCOP_1:14</a></i>;<br/>
<b>hence </b><a NAME="E7:26"/>
<span class="p1">(<span class="default"><a href="pnproc_1.html#K3" target="_self">{$}</a> <font color="Maroon">P</font></span>)</span> <a href="pnproc_1.html#K1" target="_self">multitude_of</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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