<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c4">M2</font> be    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of  <a href="hilbert3.html#K2" title="HILBERT3:func.2">SetVal</a> <font color="Maroon" title="c1">V</font>, <a href="hilbert3.html#K2" title="HILBERT3:func.2">SetVal</a> <font color="Maroon" title="c1">V</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:42_1_2"/><i><font color="Green" title="E32">A22</font></i>: 
<font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> 1
 <b>and </b><br/><a NAME="E2:42_1_2"/><i><font color="Green" title="E33">A23</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><a href="hilbert2.html#K1" title="HILBERT2:func.1">prop</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font>
 <b>and </b><br/><a NAME="E3:42_1_2"/><i><font color="Green" title="E34">A24</font></i>: 
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>   ex <font color="Olive" title="b3">p'</font> being  <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> <font color="Maroon" title="c1">V</font>,<font color="Olive" title="b1">p</font> ex <font color="Olive" title="b4">q'</font> being  <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> <font color="Maroon" title="c1">V</font>,<font color="Olive" title="b2">q</font> st <br/>( <font color="Olive" title="b3">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b4">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Olive" title="b2">q</font> &amp; <font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Olive" title="b3">p'</font>,<font color="Olive" title="b4">q'</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> &amp; <font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> )
 <b>and </b><br/><a NAME="E4:42_1_2"/><i><font color="Green" title="E35">A25</font></i>: 
<font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> 1
 <b>and </b><br/><a NAME="E5:42_1_2"/><i><font color="Green" title="E36">A26</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><a href="hilbert2.html#K1" title="HILBERT2:func.1">prop</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font>
 <b>and </b><br/><a NAME="E6:42_1_2"/><i><font color="Green" title="E37">A27</font></i>: 
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>   ex <font color="Olive" title="b3">p'</font> being  <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> <font color="Maroon" title="c1">V</font>,<font color="Olive" title="b1">p</font> ex <font color="Olive" title="b4">q'</font> being  <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> <font color="Maroon" title="c1">V</font>,<font color="Olive" title="b2">q</font> st <br/>( <font color="Olive" title="b3">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b4">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Olive" title="b2">q</font> &amp; <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Olive" title="b3">p'</font>,<font color="Olive" title="b4">q'</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span> &amp; <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <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> ] <b>means </b><font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> $1;<br/>
<a NAME="E7:42_1_2"/><i><font color="Green" title="E38">A28</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a> ]
 
<b>by </b><i><a class="txt" href="hilbert3.html#E1:42_1_2"><i><font color="Green" title="E32">A22</font></i></a>, <a class="txt" href="hilbert3.html#E4:42_1_2"><i><font color="Green" title="E35">A25</font></i></a></i>;<br/>
<a NAME="E8:42_1_2"/><i><font color="Green" title="E39">A29</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[ <a href="hilbert2.html#K1" title="HILBERT2:func.1">prop</a> <font color="Olive" title="b1">n</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<b>thus </b><font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><a href="hilbert2.html#K1" title="HILBERT2:func.1">prop</a> <font color="Maroon" title="c5">n</font></span>)</span> = 
<font color="Maroon" title="c2">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font>
<b>by </b><i><a class="txt" href="hilbert3.html#E2:42_1_2"><i><font color="Green" title="E33">A23</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><a href="hilbert2.html#K1" title="HILBERT2:func.1">prop</a> <font color="Maroon" title="c5">n</font></span>)</span>
<b>by </b><i><a class="txt" href="hilbert3.html#E5:42_1_2"><i><font color="Green" title="E36">A26</font></i></a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E9:42_1_2"/><i><font color="Green" title="E40">A30</font></i>: 
for <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">s</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 <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">s</font>] holds <br/>( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Olive" title="b2">s</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Olive" title="b2">s</font>] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">r</font>, <font color="Maroon" title="c6">s</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="E1:42_1_2_2"/><i><font color="Green" title="E41">A31</font></i>: 
( <font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c5">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c5">r</font> &amp; <font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c6">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c6">s</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c7">p'</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c5">r</font>, <font color="Maroon" title="c8">q'</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c6">s</font><b> such that </b><br/><a NAME="E3:42_1_2_2"/><i><font color="Green" title="E42">A32</font></i>: 
( <font color="Maroon" title="c7">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c5">r</font> &amp; <font color="Maroon" title="c8">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c6">s</font> )
 <b>and </b><br/><a NAME="E4:42_1_2_2"/><i><font color="Green" title="E43">A33</font></i>: 
<font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c7">p'</font>,<font color="Maroon" title="c8">q'</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span>
 <b>and </b><br/><a NAME="E5:42_1_2_2"/><i><font color="Green" title="E44">A34</font></i>: 
<font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">p'</font> <a href="hilbert3.html#K1" title="HILBERT3:func.1">=&gt;</a> <font color="Maroon" title="c8">q'</font>
 <b>by </b><i><a class="txt" href="hilbert3.html#E3:42_1_2"><i><font color="Green" title="E34">A24</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">p'</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c5">r</font>, <font color="Maroon" title="c10">q'</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c6">s</font><b> such that </b><br/><a NAME="E7:42_1_2_2"/><i><font color="Green" title="E45">A35</font></i>: 
( <font color="Maroon" title="c9">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c5">r</font> &amp; <font color="Maroon" title="c10">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <font color="Maroon" title="c6">s</font> )
 <b>and </b><br/><a NAME="E8:42_1_2_2"/><i><font color="Green" title="E46">A36</font></i>: 
<font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="funct_3.html#K16" title="FUNCT_3:func.16">[:</a><span class="default"><font color="Maroon" title="c9">p'</font>,<font color="Maroon" title="c10">q'</font></span><a href="funct_3.html#K16" title="FUNCT_3:func.16">:]</a></span>
 <b>and </b><br/><a NAME="E9:42_1_2_2"/><i><font color="Green" title="E47">A37</font></i>: 
<font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">p'</font> <a href="hilbert3.html#K1" title="HILBERT3:func.1">=&gt;</a> <font color="Maroon" title="c10">q'</font>
 <b>by </b><i><a class="txt" href="hilbert3.html#E6:42_1_2"><i><font color="Green" title="E37">A27</font></i></a></i>;<br/>
<b>thus </b><a NAME="E10:42_1_2_2"/>
<font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c6">s</font></span>)</span>
 <b>by </b><i><a class="txt" href="hilbert3.html#E1:42_1_2_2"><i><font color="Green" title="E41">A31</font></i></a>, <a class="txt" href="hilbert3.html#E3:42_1_2_2"><i><font color="Green" title="E42">A32</font></i></a>, <a class="txt" href="hilbert3.html#E4:42_1_2_2"><i><font color="Green" title="E43">A33</font></i></a>, <a class="txt" href="hilbert3.html#E7:42_1_2_2"><i><font color="Green" title="E45">A35</font></i></a>, <a class="txt" href="hilbert3.html#E8:42_1_2_2"><i><font color="Green" title="E46">A36</font></i></a></i>;<br/>

<b>thus </b><a NAME="E11:42_1_2_2"/>
<font color="Maroon" title="c3">M1</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c6">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> <a href="msualg_3.html#K1" title="MSUALG_3:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c6">s</font></span>)</span>
 <b>by </b><i><a class="txt" href="hilbert3.html#E1:42_1_2_2"><i><font color="Green" title="E41">A31</font></i></a>, <a class="txt" href="hilbert3.html#E3:42_1_2_2"><i><font color="Green" title="E42">A32</font></i></a>, <a class="txt" href="hilbert3.html#E5:42_1_2_2"><i><font color="Green" title="E44">A34</font></i></a>, <a class="txt" href="hilbert3.html#E7:42_1_2_2"><i><font color="Green" title="E45">A35</font></i></a>, <a class="txt" href="hilbert3.html#E9:42_1_2_2"><i><font color="Green" title="E47">A37</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:42_1_2"/>
for <font color="Olive" title="b1">r</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>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>]
 
<b>from </b><i><a class="ref" href="hilbert2.html#S2" title="HILBERT2:sch.2">HILBERT2:sch 2</a>(<a class="txt" href="hilbert3.html#E7:42_1_2"><i><font color="Green" title="E38">A28</font></i></a>, <a class="txt" href="hilbert3.html#E8:42_1_2"><i><font color="Green" title="E39">A29</font></i></a>, <a class="txt" href="hilbert3.html#E9:42_1_2"><i><font color="Green" title="E40">A30</font></i></a>);<br/></i>
<a NAME="E11:42_1_2"/><b>then </b>
for <font color="Olive" title="b1">r</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K1" title="HILBERT1:func.1">HP-WFF</a>  holds <br/><font color="Maroon" title="c3">M1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">r</font>
 
;<br/>
<b>hence </b><a NAME="E12:42_1_2"/>
<font color="Maroon" title="c3">M1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c4">M2</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>;<br/>


</div>
