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

<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="hilbert1.html#K1">HP-WFF</a> ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="hilbert1.html#K1">HP-WFF</a> ] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> is <a href="hilbert2.html#V1" target="_self">conjunctive</a> or <font color="Maroon">a<sub>1</sub></font> is <a href="hilbert2.html#V2" target="_self">conditional</a> or <font color="Maroon">a<sub>1</sub></font> is <a href="hilbert2.html#V3" target="_self">simple</a> or <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="hilbert1.html#K2">VERUM</a>  );<br/>
<a NAME="E1:18"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="hilbert1.html#K2">VERUM</a> ]
 
;<br/>
<a NAME="E2:18"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[ <a href="hilbert2.html#K1" target="_self">prop</a> <font color="Olive">n</font>]
 
<b>by </b><i/>;<br/>
<a NAME="E3:18"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">r</font>, <font color="Olive">s</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="hilbert1.html#K1">HP-WFF</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">r</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">s</font>] holds <br/>( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">r</font> <a href="hilbert1.html#K4">'&amp;'</a> <font color="Olive">s</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">r</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Olive">s</font>] )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:18"/>
for <font color="Olive">p</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="hilbert1.html#K1">HP-WFF</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>]
 
<b>from </b><i><a class="ref" href="hilbert2.html#S2" target="_self">HILBERT2:sch 2</a>(, , );<br/></i>
<b>hence </b><a NAME="E5:18"/>
( <font color="Maroon">p</font> is <a href="hilbert2.html#V1" target="_self">conjunctive</a> or <font color="Maroon">p</font> is <a href="hilbert2.html#V2" target="_self">conditional</a> or <font color="Maroon">p</font> is <a href="hilbert2.html#V3" target="_self">simple</a> or <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="hilbert1.html#K2">VERUM</a>  )
 ;<br/>


</div>
