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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">P</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM2">Permutation</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:83"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:83"/>
( <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:83"/><b>then </b>
( <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">P</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">P</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T4" target="_self">Th4</a>, , <a class="ref" href="funct_1.html#T146">FUNCT_1:146</a>, <a class="ref" href="funct_1.html#T152">FUNCT_1:152</a></i>;<br/>
<b>hence </b><a NAME="E4:83"/>
( <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <font color="Maroon">P</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> &amp; <font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">P</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> )
 <b>by </b><i><a class="ref" href="funct_2.html#T4" target="_self">Th4</a>, <a class="ref" href="funct_1.html#T147">FUNCT_1:147</a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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