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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">Th25</font></span>: <a NAME="T26"><span class="comment"><font color="firebrick">:: HILBERT3:26</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">P</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b4">Q</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <font color="Olive" title="b2">B</font><br/>  for <font color="Olive" title="b5">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">P</font> <a href="hilbert3.html#K1" title="HILBERT3:func.1">=&gt;</a> <font color="Olive" title="b4">Q</font></span>)</span> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">Q</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">P</font></div></div>
