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<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="hilbert1.html#K5" title="HILBERT1:func.5">CnPos</a> <font color="Maroon" title="c1">X</font> is  <a href="hilbert1.html#V6" title="HILBERT1:attr.6">Hilbert_theory</a> </span><br/>

<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert1.html#T1" target="_self" title="HILBERT1:th.1">Th1</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="hilbert1.html#D10" target="_self" title="HILBERT1:def.10">HILBERT1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">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 <br/> ( <font color="Olive" title="b1">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Olive" title="b1">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> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">q</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Olive" title="b3">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="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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<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="b3">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> &amp; <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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Olive" title="b1">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; <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="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Olive" title="b2">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> &amp; <font color="Olive" title="b1">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">q</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<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></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> &amp; ( <font color="Olive" title="b1">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="Olive" title="b1">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Olive" title="b2">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="Olive" title="b2">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> ) )</span><br/>

<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; ( <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> ) )</span><br/>





<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert1.html#T4" target="_self" title="HILBERT1:th.4">Th4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> &amp; <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> &amp; <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> &amp; <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> &amp; ( <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> ) )</span><br/>

<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert1.html#T3" target="_self" title="HILBERT1:th.3">Th3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> &amp; <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> &amp; <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> &amp; ( <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> ) )</span><br/>

<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert1.html#T5" target="_self" title="HILBERT1:th.5">Th5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> &amp; <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> &amp; ( <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> ) )</span><br/>

<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert1.html#T6" target="_self" title="HILBERT1:th.6">Th6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> &amp; ( <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> ) )</span><br/>

<span class="kw">thus </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert1.html#T2" target="_self" title="HILBERT1:th.2">Th2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> )</span><br/>

<span class="kw">thus </span><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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert1.html#T7" target="_self" title="HILBERT1:th.7">Th7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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