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<b>let </b><font color="Maroon">N</font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="ami_1.html#V2" target="_self">void</a>  <a href="ami_1.html#L1" target="_self">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="ami_1.html#M1" target="_self">FinPartState</a> of <font color="Maroon">S</font>;<br/>







<a NAME="E1:97"/>
(  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5" target="_self">Object-Kind</a> of <font color="Maroon">S</font> <a href="tarski.html#R1">c=</a>  <a href="ami_1.html#K7" target="_self">sproduct</a> the <a href="ami_1.html#U5" target="_self">Object-Kind</a> of <font color="Maroon">S</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5" target="_self">Object-Kind</a> of <font color="Maroon">S</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:97"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="ami_1.html#K7" target="_self">sproduct</a> the <a href="ami_1.html#U5" target="_self">Object-Kind</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="ami_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E3:97"/><i><font color="Green">E34</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<a NAME="E4:97"/>
<font color="Maroon">p</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="ami_1.html#D14" target="_self">Def14</a></i>;<br/>
<a NAME="E5:97"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T29">FINSET_1:29</a></i>;<br/>
<a NAME="E6:97"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span></span>)</span> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i>, <a class="ref" href="finset_1.html#T15">FINSET_1:15</a></i>;<br/>
<a NAME="E7:97"/><b>then </b>
<font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span> is <a href="finset_1.html#V1">finite</a>
 
<b>by </b><i><a class="ref" href="finset_1.html#T29">FINSET_1:29</a></i>;<br/>
<b>hence </b><a NAME="E8:97"/>
<font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font></span>)</span> is    <a href="ami_1.html#M1" target="_self">FinPartState</a> of <font color="Maroon">S</font>
 <b>by </b><i>, <a class="ref" href="ami_1.html#D14" target="_self">Def14</a></i>;<br/>


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