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<b>let </b><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_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">x</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="E1:34"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3" target="_self">"</a> <font color="Maroon">f</font></span>)</span> <a href="relat_1.html#K9">.:</a> <font color="Maroon">B</font>
 ;<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="E3:34"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">Y</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_3.html#K3" target="_self">"</a> <font color="Maroon">f</font></span>)</span>
 <b>and </b><br/><a NAME="E4:34"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E5:34"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="funct_3.html#K3" target="_self">"</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D12">FUNCT_1:def 12</a></i>;<br/>
<a NAME="E6:34"/>
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:34"/><b>then </b>
( <span class="p1">(<span class="default"><a href="funct_3.html#K3" target="_self">"</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relat_1.html#K10">"</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E8:34"/><b>then </b>
( <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <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="funct_1.html#T147">FUNCT_1:147</a>, <a class="ref" href="relat_1.html#T167">RELAT_1:167</a></i>;<br/>
<a NAME="E9:34"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 
;<br/>
<a NAME="E10:34"/><b>then </b>
( <font color="Maroon">x</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_3.html#K1" target="_self">.:</a> <font color="Maroon">f</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_3.html#K1" target="_self">.:</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E11:34"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="funct_3.html#K1" target="_self">.:</a> <font color="Maroon">f</font></span>)</span> <a href="relat_1.html#K10">"</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>


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