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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Lm3</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: HILBERT4:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="hilbert3.html#NM1" title="HILBERT3:NM.1">SetValuation</a><br/>  for <font color="Olive" title="b2">P</font> being    <a href="hilbert3.html#M1" title="HILBERT3:mode.1">Permutation</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">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>   st  <a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> (<font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">p</font>) is  <a href="abian.html#V2" title="ABIAN:attr.2">with_fixpoint</a>  &amp;  <a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> (<font color="Olive" title="b2">P</font>,<font color="Olive" title="b4">q</font>) is  <a href="abian.html#NV5" title="ABIAN:NV.5">without_fixpoints</a>  holds <br/> <a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> (<font color="Olive" title="b2">P</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Olive" title="b4">q</font></span>)</span>) is  <a href="abian.html#NV5" title="ABIAN:NV.5">without_fixpoints</a> </div></div>
