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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E31">Th38</font></span>: <a NAME="T39"><span class="comment"><font color="firebrick">:: HILBERT3:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="hilbert1.html#K1" title="HILBERT1:func.1">HP-WFF</a> <br/>  for <font color="Olive" title="b3">V</font> being   <a href="hilbert3.html#NM1" title="HILBERT3:NM.1">SetValuation</a><br/>  for <font color="Olive" title="b4">P</font> being    <a href="hilbert3.html#M1" title="HILBERT3:mode.1">Permutation</a> of <font color="Olive" title="b3">V</font><br/>  for <font color="Olive" title="b5">f</font>, <font color="Olive" title="b6">g</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> (<font color="Olive" title="b3">V</font>,<font color="Olive" title="b1">p</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> (<font color="Olive" title="b3">V</font>,<font color="Olive" title="b2">q</font>)</span>)</span>  st <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> (<font color="Olive" title="b4">P</font>,<span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Olive" title="b2">q</font></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">g</font> holds <br/><span class="p1">(<span class="default"><a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> (<font color="Olive" title="b4">P</font>,<font color="Olive" title="b2">q</font>)</span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b6">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b5">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> (<font color="Olive" title="b4">P</font>,<font color="Olive" title="b1">p</font>)</span>)</span></div></div>
