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<b>let </b><font color="Maroon">D</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> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">Z</font>,<font color="Maroon">S</font></span><a href="zfmisc_1.html#K4">:]</a></span>,<font color="Maroon">D</font>, <font color="Maroon">f2</font> be   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">Z</font>,<font color="Maroon">S</font></span><a href="zfmisc_1.html#K4">:]</a></span>,<font color="Maroon">D</font>;<br/>











<b>assume </b><a NAME="E1:13"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font>, <font color="Olive">s</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">z</font>,<font color="Olive">s</font></span><a href="mcart_1.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">z</font>,<font color="Olive">s</font></span><a href="mcart_1.html#K4">]</a></span>
 ;<br/>

<a NAME="E2:13"/>
for <font color="Olive">t</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">Z</font>,<font color="Maroon">S</font></span><a href="zfmisc_1.html#K4">:]</a></span> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">t</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">t</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:13_1"/>
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K4">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">Z</font>,<font color="Maroon">S</font></span><a href="zfmisc_1.html#K4">:]</a></span>
 ;<br/>

<a NAME="E2:13_1"/><b>then </b>
 ex <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font>, <font color="Olive">s</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> &amp; <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">z</font>,<font color="Olive">s</font></span><a href="mcart_1.html#K4">]</a></span> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T83">MCART_1:83</a></i>;<br/>
<b>hence </b><a NAME="E3:13_1"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">t</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:13"/>
<font color="Maroon">f1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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