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<b>let </b><font color="Maroon">X</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="hilbert1.html#K1" target="_self">HP-WFF</a> ;<br/>

<b>thus </b><a NAME="E1:30"/>
 <a href="hilbert1.html#K2" target="_self">VERUM</a>  <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K5" target="_self">CnPos</a> <font color="Maroon">X</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="hilbert1.html#D10" target="_self">HILBERT1:def 10</a><br/>

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





<b>thus </b><a NAME="E2:30"/>
<font color="Maroon">p</font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K5" target="_self">CnPos</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="hilbert1.html#D2" target="_self">Def2</a></i>;<br/>

<b>thus </b><a NAME="E3:30"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K5" target="_self">CnPos</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="hilbert1.html#D1" target="_self">Def1</a></i>;<br/>

<b>thus </b><a NAME="E4:30"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K5" target="_self">CnPos</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E5:30"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K5" target="_self">CnPos</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E6:30"/>
<font color="Maroon">p</font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K5" target="_self">CnPos</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E7:30"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K5" target="_self">CnPos</a> <font color="Maroon">X</font> &amp; <font color="Maroon">p</font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K5" target="_self">CnPos</a> <font color="Maroon">X</font> implies <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K5" target="_self">CnPos</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="hilbert1.html#D3" target="_self">Def3</a></i>;<br/>


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