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

<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> ,   <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> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>$5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>($3,$4);<br/>
<b>defpred </b><font color="Maroon">S<sub>2</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> ,   <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> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>$5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>($3,$4);<br/>
<a NAME="E1:40_1"/><i><font color="Green" title="E31">A1</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> <br/> for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   ex <font color="Olive" title="b5">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">c</font>]
 
;<br/>
<a NAME="E2:40_1"/><i><font color="Green" title="E32">A2</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> <br/> for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   ex <font color="Olive" title="b5">d</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">d</font>]
 
;<br/>
<a NAME="E3:40_1"/><i><font color="Green" title="E33">A3</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> <br/> for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">d</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">c</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b6">d</font>] holds <br/><font color="Olive" title="b5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">d</font>
 
;<br/>
<a NAME="E4:40_1"/><i><font color="Green" title="E34">A4</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> <br/> for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">d</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">c</font>] &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b6">d</font>] holds <br/><font color="Olive" title="b5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">d</font>
 
;<br/>
<b>consider </b><font color="Maroon" title="c1">M</font> being    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of  <a href="hilbert1.html#K1" title="HILBERT1:func.1">HP-WFF</a> <b> such that </b><br/><a NAME="E6:40_1"/><i><font color="Green" title="E35">A5</font></i>: 
<font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E7:40_1"/><i><font color="Green" title="E36">A6</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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">F<sub>2</sub></font>(<font color="Olive" title="b1">n</font>)
 <b>and </b><br/><a NAME="E8:40_1"/><i><font color="Green" title="E37">A7</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>  holds <br/> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">q</font>,<font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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>] &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">q</font>,<font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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>] )
 <b>from </b><i><a class="ref" href="hilbert2.html#S3" target="_self" title="HILBERT2:sch.3">HILBERT2:sch 3</a>(<a class="txt" href="hilbert2.html#E1:40_1"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="hilbert2.html#E2:40_1"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="hilbert2.html#E3:40_1"><i><font color="Green" title="E33">A3</font></i></a>, <a class="txt" href="hilbert2.html#E4:40_1"><i><font color="Green" title="E34">A4</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c1">M</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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">F<sub>2</sub></font>(<font color="Olive" title="b1">n</font>) ) &amp; ( 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>  holds <br/> ( <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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> <font color="Maroon">F<sub>3</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">q</font></span>)</span>) &amp; <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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="Maroon">F<sub>4</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">q</font></span>)</span>) ) ) )</span><br/>

<b>thus </b><a NAME="E9:40_1"/>
<font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>by </b><i><a class="txt" href="hilbert2.html#E6:40_1"><i><font color="Green" title="E35">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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">F<sub>2</sub></font>(<font color="Olive" title="b1">n</font>) ) &amp; ( 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>  holds <br/> ( <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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> <font color="Maroon">F<sub>3</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">q</font></span>)</span>) &amp; <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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="Maroon">F<sub>4</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">q</font></span>)</span>) ) ) )</span><br/>

<b>thus </b><a NAME="E10:40_1"/>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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">F<sub>2</sub></font>(<font color="Olive" title="b1">n</font>)
 <b>by </b><i><a class="txt" href="hilbert2.html#E7:40_1"><i><font color="Green" title="E36">A6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 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>  holds <br/> ( <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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> <font color="Maroon">F<sub>3</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">q</font></span>)</span>) &amp; <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1: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="Maroon">F<sub>4</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">q</font></span>)</span>) )</span><br/>

<b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">q</font></span>)</span>) &amp; <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">q</font></span>)</span>) )</span><br/>



<b>set </b><font color="Maroon" title="c4">x</font> = <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">p</font>;<br/>
<b>set </b><font color="Maroon" title="c5">y</font> = <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">q</font>;<br/>
<b>thus </b><a NAME="E11:40_1"/>
<font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">q</font></span>)</span>)
 <b>by </b><i><a class="txt" href="hilbert2.html#E8:40_1"><i><font color="Green" title="E37">A7</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">q</font></span>)</span>)</span><br/>

<b>thus </b><a NAME="E12:40_1"/>
<font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">p</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">q</font></span>)</span>)
 <b>by </b><i><a class="txt" href="hilbert2.html#E8:40_1"><i><font color="Green" title="E37">A7</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
