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<b>let </b><font color="Maroon">F</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">G</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E1:20"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">F</font>,<font color="Maroon">G</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 ;<br/>

<b>let </b><font color="Maroon">x1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:20"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 <b>and </b><br/><a NAME="E3:20"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 <b>and </b><br/><a NAME="E4:20"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x2</font>
 ;<br/>

<b>consider </b><font color="Maroon">H</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E6:20"/><i><font color="Green">E41</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font> &amp; <font color="Maroon">H</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">H</font> )
 <b>by </b><i>, <a class="ref" href="rfinseq.html#T3">RFINSEQ:3</a></i>;<br/>
<a NAME="E7:20"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font> &amp; <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font> )
 
<b>by </b><i>, , , <a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<a NAME="E8:20"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font>
 
<b>by </b><i>, , , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<a NAME="E9:20"/>
( <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font></span>)</span> &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font></span>)</span> )
 
<b>by </b><i>, , , <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<b>hence </b><a NAME="E10:20"/>
 ex <font color="Olive">z1</font>, <font color="Olive">z2</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">z1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font> &amp; <font color="Olive">z2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">G</font> &amp; <font color="Olive">z1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">z2</font> &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Olive">z1</font> &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="funct_1.html#K1">.</a> <font color="Olive">z2</font> )
 <b>by </b><i>, </i>;<br/>


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