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<b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">B</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">C</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:84"/><i><font color="Green">E34</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E2:84"/><i><font color="Green">E36</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E3:84"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">B</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C</font>
 ;<br/>

<a NAME="E4:84"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E5:84"/><b>then </b><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E6:84"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B</font>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E7:84"/><b>then </b>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E8:84"/><b>then </b>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">B</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<a NAME="E9:84"/><b>then </b>
<font color="Maroon">g</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">B</font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="xboole_0.html#K1">{}</a> , <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#T55">FUNCT_2:55</a></i>;<br/>
<a NAME="E10:84"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">g</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="partfun1.html#T57">PARTFUN1:57</a></i>;<br/>
<a NAME="E11:84"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_4.html#T12" target="_self">Th12</a>, <a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<a NAME="E12:84"/><b>then </b>
<font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">C</font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="xboole_0.html#K1">{}</a> , <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#T55">FUNCT_2:55</a></i>;<br/>
<a NAME="E13:84"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="partfun1.html#T57">PARTFUN1:57</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_4.html#K1" target="_self">+*</a> <font color="Maroon">g</font></span>)</span> <a href="relat_1.html#K7">|</a> <font color="Maroon">B</font> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">B</font></span>)</span> <a href="funct_4.html#K1" target="_self">+*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">B</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T6" target="_self">Th6</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">B</font>
<b>by </b><i><a class="ref" href="funct_4.html#T13" target="_self">Th13</a>, </i>
<br/>.= 
<font color="Maroon">f</font>
<b>by </b><i>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_4.html#K1" target="_self">+*</a> <font color="Maroon">g</font></span>)</span> <a href="relat_1.html#K7">|</a> <font color="Maroon">C</font> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">C</font></span>)</span> <a href="funct_4.html#K1" target="_self">+*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">C</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T6" target="_self">Th6</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">C</font>
<b>by </b><i><a class="ref" href="funct_4.html#T14" target="_self">Th14</a>, </i>
<br/>.= 
<font color="Maroon">g</font>
<b>by </b><i>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>
;<br/>


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