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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></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">E46</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:84"/><i><font color="Green">E47</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E3:84"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E4:84"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="funct_4.html#E1:84"><i><font color="Green">E46</font></i></a>, <a class="txt" href="funct_4.html#E3:84"><i><font color="Green">E48</font></i></a>, <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">E49</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="funct_4.html#E2:84"><i><font color="Green">E47</font></i></a>, <a class="txt" href="funct_4.html#E3:84"><i><font color="Green">E48</font></i></a>, <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">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>3</sub></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">E50</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="funct_4.html#E5:84"><i><font color="Green">E49</font></i></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">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>4</sub></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">E51</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font> <a href="funct_4.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_4.html#K1" target="_self">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T75" target="_self">Th75</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="funct_4.html#E10:84"><i><font color="Green">E50</font></i></a>, <a class="ref" href="funct_4.html#T22" target="_self">Th22</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="funct_4.html#E1:84"><i><font color="Green">E46</font></i></a>, <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">c<sub>1</sub></font> <a href="funct_4.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_4.html#K1" target="_self">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T75" target="_self">Th75</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="funct_4.html#E13:84"><i><font color="Green">E51</font></i></a>, <a class="ref" href="funct_4.html#T21" target="_self">Th21</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="funct_4.html#E2:84"><i><font color="Green">E47</font></i></a>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>
;<br/>


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