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<b>let </b><font color="Maroon" title="c1">p</font> be    <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/>

<b>assume </b><a NAME="E1:63_1_1"/><i><font color="Green" title="E49">A1</font></i>: 
<font color="Maroon" title="c1">p</font> is <a href="hilbert3.html#V1" title="HILBERT3:attr.1">canonical</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c2">V</font> be   <a href="hilbert3.html#NM1" title="HILBERT3:NM.1">SetValuation</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="hilbert3.html#D8" target="_self" title="HILBERT3:def.8">HILBERT3:def 8</a><br/>

<b>consider </b><font color="Maroon" title="c3">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:63_1_1"/><i><font color="Green" title="E50">A2</font></i>: 
for <font color="Olive" title="b1">P</font> being   <a href="hilbert3.html#M1" title="HILBERT3:mode.1">Permutation</a> of <font color="Maroon" title="c2">V</font> holds  <font color="Maroon" title="c3">x</font> <a href="abian.html#R1" title="ABIAN:pred.1">is_a_fixpoint_of</a>  <a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> <font color="Olive" title="b1">P</font>,<font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="hilbert3.html#E1:63_1_1"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="hilbert3.html#D7" target="_self" title="HILBERT3:def.7">Def7</a></i>;<br/>
<b>let </b><font color="Maroon" title="c4">P</font> be    <a href="hilbert3.html#M1" title="HILBERT3:mode.1">Permutation</a> of <font color="Maroon" title="c2">V</font>;<br/>

<b>take </b>
<font color="Maroon" title="c3">x</font>
;<br/>

<b>thus </b><a NAME="E4:63_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="abian.html#R1" title="ABIAN:pred.1">is_a_fixpoint_of</a>  <a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="hilbert3.html#E3:63_1_1"><i><font color="Green" title="E50">A2</font></i></a></i>;<br/>


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