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<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">g</font>, <font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">h</font> be   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <font color="Maroon" title="c1">A</font>;<br/>







<b>assume </b><a NAME="E1:8"/>
<font color="Maroon" title="c2">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">h</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">f</font>
 ;<br/>

<a NAME="E2:8"/><b>then </b>
<font color="Maroon" title="c2">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">h</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>;<br/>
<a NAME="E3:8"/><b>then </b>
<font color="Maroon" title="c2">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">h</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>;<br/>
<a NAME="E4:8"/><b>then </b>
<font color="Maroon" title="c2">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">h</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T88" title="FUNCT_2:th.88">FUNCT_2:88</a></i>;<br/>
<a NAME="E5:8"/><b>then </b>
<font color="Maroon" title="c2">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">h</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T88" title="FUNCT_2:th.88">FUNCT_2:88</a></i>;<br/>
<a NAME="E6:8"/><b>then </b>
<font color="Maroon" title="c2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">h</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></i>;<br/>
<b>hence </b><a NAME="E7:8"/>
<font color="Maroon" title="c2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">h</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></i>;<br/>


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