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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="funct_2.html#NM2">Permutation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:8"/>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:8"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="transgeo.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>
<a NAME="E3:8"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>
<a NAME="E4:8"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K2">"</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T88">FUNCT_2:88</a></i>;<br/>
<a NAME="E5:8"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T88">FUNCT_2:88</a></i>;<br/>
<a NAME="E6:8"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="transgeo.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>;<br/>
<b>hence </b><a NAME="E7:8"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>;<br/>


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