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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E1:9"/><i><font color="Green">E7</font></i>: 
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<i><font color="Green">E8</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="funct_6.html#K6">:&gt;</a></span> = 
 <a href="funct_6.html#K4">meet</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2">doms</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_6.html#T49">FUNCT_6:49</a></i>
<br/>.= 
 <a href="setfam_1.html#K1">meet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="funct_6.html#K2">doms</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_6.html#D4">FUNCT_6:def 4</a></i>
;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:9"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="txt" href="comput_1.html#E1:9"><i><font color="Green">E7</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E5:9"/><i><font color="Green">E10</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2">doms</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K10">"</a> <span class="p1">(<span class="default"><a href="funct_6.html#K1">SubFuncs</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_6.html#D2">FUNCT_6:def 2</a></i>;<br/>
<a NAME="E6:9"/><b>then </b><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2">doms</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="comput_1.html#E4:9"><i><font color="Green">E9</font></i></a>, <a class="ref" href="funct_6.html#T28">FUNCT_6:28</a></i>;<br/>
<a NAME="E7:9"/><b>then </b>
<span class="p1">(<span class="default"><a href="funct_6.html#K2">doms</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="comput_1.html#E4:9"><i><font color="Green">E9</font></i></a>, <a class="txt" href="comput_1.html#E5:9"><i><font color="Green">E10</font></i></a>, <a class="ref" href="funct_5.html#T10">FUNCT_5:10</a>, <a class="ref" href="funct_6.html#D2">FUNCT_6:def 2</a></i>;<br/>
<a NAME="E8:9"/><b>then </b>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_6.html#K2">doms</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="comput_1.html#E6:9"><i><font color="Green">E11</font></i></a>, <a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<a NAME="E9:9"/><b>then </b>
 <a href="setfam_1.html#K1">meet</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="funct_6.html#K2">doms</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="setfam_1.html#T5">SETFAM_1:5</a></i>;<br/>
<b>hence </b><a NAME="E10:9"/>
<span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="funct_6.html#K6">:&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="comput_1.html#E2:9"><i><font color="Green">E8</font></i></a>, <a class="ref" href="relat_1.html#T64">RELAT_1:64</a></i>;<br/>


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