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<b>let </b><font color="Maroon" title="c1">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#D7" target="_self" title="HILBERT3:def.7">HILBERT3:def 7</a><br/>

<b>take </b>
0
;<br/>

<b>let </b><font color="Maroon" title="c2">P</font> be    <a href="hilbert3.html#M1" title="HILBERT3:mode.1">Permutation</a> of <font color="Maroon" title="c1">V</font>;<br/>

<a NAME="E1:53_1_1"/><i><font color="Green" title="E37">A1</font></i>: 
 <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> <font color="Maroon" title="c1">V</font>,<a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="hilbert3.html#D2" target="_self" title="HILBERT3:def.2">Def2</a></i>;<br/>
<a NAME="E2:53_1_1"/>
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 1
 
<b>by </b><i><a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:53_1_1"/>
0 <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="c2">P</font>,<a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a> 
 <b>by </b><i><a class="txt" href="hilbert3.html#E1:53_1_1"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="hilbert3.html#T3" target="_self" title="HILBERT3:th.3">Th3</a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a></i>;<br/>


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