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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>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">p</font>, <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">q</font>, <font color="Maroon">g</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">p</font>, <a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">q</font>;<br/>









<b>assume </b><a NAME="E1:50"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">P</font>,<span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">g</font>
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">P</font>,<font color="Maroon">q</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font> = 
<span class="p1">(<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">q</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default"><a href="hilbert3.html#K3" target="_self">SetVal</a> <font color="Maroon">V</font>,<font color="Maroon">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>
<br/>.= 
<span class="p1">(<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">q</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">P</font>,<font color="Maroon">p</font></span>)</span> <a href="funct_2.html#K2">"</a> </span>)</span> <a href="partfun1.html#K1">*</a> <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>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T88">FUNCT_2:88</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">P</font>,<font color="Maroon">q</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">g</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">P</font>,<font color="Maroon">p</font></span>)</span> <a href="funct_2.html#K2">"</a> </span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">P</font>,<font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K5" target="_self">Perm</a> <font color="Maroon">P</font>,<font color="Maroon">p</font></span>)</span>
<b>by </b><i>, </i>
;<br/>


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