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<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">B</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/>



<b>assume </b><a NAME="E1:14"/>
<font color="Maroon">f</font> is <a href="funct_2.html#V2">onto</a>
 ;<br/>

<a NAME="E2:14"/><b>then </b><i><font color="Green">E20</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<b>let </b><font color="Maroon">xx</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:14"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">xx</font> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">B</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">x'</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:14"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">xx</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x'</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="relat_1.html#D1">RELAT_1:def 1</a></i>;<br/>
<a NAME="E6:14"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x'</font>
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>
<a NAME="E7:14"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>
<b>then consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E9:14"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E10:14"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="funct_2.html#T17">FUNCT_2:17</a></i>;<br/>
<a NAME="E11:14"/><i><font color="Green">E36</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E12:14"/><i><font color="Green">E37</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>
<a NAME="E13:14"/>
<span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">f</font></span><a href="funct_3.html#K16">:]</a></span> <a href="binop_1.html#K1">.</a> <font color="Maroon">y</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">xx</font>
 
<b>by </b><i>, , , , , <a class="ref" href="funct_3.html#D9">FUNCT_3:def 9</a></i>;<br/>
<b>hence </b><a NAME="E14:14"/>
<font color="Maroon">xx</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">f</font></span><a href="funct_3.html#K16">:]</a></span> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="functor0.html#E2:14"><i><font color="Green">E20</font></i></a>, <a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/>


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