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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">SD</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">D</font>,<font color="Maroon">D</font>;<br/>







<b>assume </b><a NAME="E1:8"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">SD</font>
 ;<br/>

<a NAME="E2:8"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">SD</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:8"/><b>then </b><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><a href="partfun2.html#K1" target="_self">id</a> <font color="Maroon">SD</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:8"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="partfun2.html#K1" target="_self">id</a> <font color="Maroon">SD</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<a NAME="E5:8"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="partfun2.html#K1" target="_self">id</a> <font color="Maroon">SD</font></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:8"/>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="partfun2.html#K1" target="_self">id</a> <font color="Maroon">SD</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T38">FUNCT_1:38</a></i>;<br/>
<a NAME="E7:8"/><b>then </b>
<font color="Maroon">F</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="partfun2.html#K1" target="_self">id</a> <font color="Maroon">SD</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>hence </b><a NAME="E8:8"/>
<font color="Maroon">F</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="partfun2.html#K1" target="_self">id</a> <font color="Maroon">SD</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>


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