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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="hilbert1.html#K1" title="HILBERT1:func.1">HP-WFF</a> ;<br/>

<b>thus </b><a NAME="E1:30"/>
 <a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K5" title="HILBERT1:func.5">CnPos</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="hilbert1.html#T1" target="_self" title="HILBERT1:th.1">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="hilbert1.html#D10" target="_self" title="HILBERT1:def.10">HILBERT1:def 10</a><br/>

<b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</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>thus </b><a NAME="E2:30"/>
<font color="Maroon" title="c2">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K5" title="HILBERT1:func.5">CnPos</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="hilbert1.html#T4" target="_self" title="HILBERT1:th.4">Th4</a></i>;<br/>

<b>thus </b><a NAME="E3:30"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c4">r</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<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="c4">r</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K5" title="HILBERT1:func.5">CnPos</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="hilbert1.html#T3" target="_self" title="HILBERT1:th.3">Th3</a></i>;<br/>

<b>thus </b><a NAME="E4:30"/>
<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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K5" title="HILBERT1:func.5">CnPos</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="hilbert1.html#T5" target="_self" title="HILBERT1:th.5">Th5</a></i>;<br/>

<b>thus </b><a NAME="E5:30"/>
<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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K5" title="HILBERT1:func.5">CnPos</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="hilbert1.html#T6" target="_self" title="HILBERT1:th.6">Th6</a></i>;<br/>

<b>thus </b><a NAME="E6:30"/>
<font color="Maroon" title="c2">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<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></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K5" title="HILBERT1:func.5">CnPos</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="hilbert1.html#T2" target="_self" title="HILBERT1:th.2">Th2</a></i>;<br/>

<b>thus </b><a NAME="E7:30"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K5" title="HILBERT1:func.5">CnPos</a> <font color="Maroon" title="c1">X</font> &amp; <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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K5" title="HILBERT1:func.5">CnPos</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="hilbert1.html#K5" title="HILBERT1:func.5">CnPos</a> <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="ref" href="hilbert1.html#T7" target="_self" title="HILBERT1:th.7">Th7</a></i>;<br/>


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