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<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="hilbert1.html#K1">HP-WFF</a> ;<br/><b>let </b><font color="Maroon">q</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="hilbert1.html#K1">HP-WFF</a> ;<br/><b>let </b><font color="Maroon">V</font> be   <a href="hilbert3.html#NM1">SetValuation</a>;<br/><b>let </b><font color="Maroon">P</font> be    <a href="hilbert3.html#M1" target="_self">Permutation</a> of <font color="Maroon">V</font>;<br/>







<b>consider </b><font color="Maroon">p'</font> being   <a href="funct_2.html#NM2">Permutation</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">p</font>, <font color="Maroon">q'</font> being   <a href="funct_2.html#NM2">Permutation</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">q</font><b> such that </b><br/><a NAME="E2:45"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">p'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K4" target="_self">Perm</a> <font color="Maroon">P</font></span>)</span> <a href="msualg_3.html#K1">.</a> <font color="Maroon">p</font> &amp; <font color="Maroon">q'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K4" target="_self">Perm</a> <font color="Maroon">P</font></span>)</span> <a href="msualg_3.html#K1">.</a> <font color="Maroon">q</font> )
 <b>and </b><br/><a NAME="E3:45"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><a href="hilbert3.html#K4" target="_self">Perm</a> <font color="Maroon">P</font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K4">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">p'</font>,<font color="Maroon">q'</font></span><a href="funct_3.html#K16">:]</a></span>
 <b>and </b><br/><a NAME="E4:45"/>
<span class="p1">(<span class="default"><a href="hilbert3.html#K4" target="_self">Perm</a> <font color="Maroon">P</font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p'</font> <a href="hilbert3.html#K1" target="_self">=&gt;</a> <font color="Maroon">q'</font>
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E5:45"/>
 <a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">P</font>,<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K4">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="funct_2.html#R1">=</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><span class="p2">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">P</font>,<font color="Maroon">p</font></span>)</span>,<span class="p2">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">P</font>,<font color="Maroon">q</font></span>)</span></span><a href="funct_3.html#K16">:]</a></span>
 <b>by </b><i>, </i>;<br/>


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