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<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">B</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</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="funct_1.html#D8">FUNCT_1:def 8</a><br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:9"/><i><font color="Green">E23</font></i>: 
( <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="pralg_1.html#K6" target="_self">Inv</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span> &amp; <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="pralg_1.html#K6" target="_self">Inv</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="pralg_1.html#K6" target="_self">Inv</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pralg_1.html#K6" target="_self">Inv</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">x</font>, <font color="Maroon">y1</font> = <font color="Maroon">y</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span> <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E3:9"/>
( <span class="p1">(<span class="default"><a href="pralg_1.html#K6" target="_self">Inv</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="domain_1.html#K3">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="domain_1.html#K2">`1</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> &amp; <span class="p1">(<span class="default"><a href="pralg_1.html#K6" target="_self">Inv</a> <font color="Maroon">A</font>,<font color="Maroon">B</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="domain_1.html#K3">`2</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">y1</font> <a href="domain_1.html#K2">`1</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> )
 
<b>by </b><i/>;<br/>
<a NAME="E4:9"/><b>then </b>
( <font color="Maroon">x1</font> <a href="domain_1.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> <a href="domain_1.html#K2">`1</a>  &amp; <font color="Maroon">x1</font> <a href="domain_1.html#K3">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> <a href="domain_1.html#K3">`2</a>  )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E5:9"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="domain_1.html#T12">DOMAIN_1:12</a></i>;<br/>


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