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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</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">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">HP-WFF</a> ;<br/>





<a NAME="E1:33"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">p</font> <a href="hilbert1.html#K4">'&amp;'</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">2</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>;<br/>
<a NAME="E2:33"/><i><font color="Green">E30</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K4">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 2 &amp; <span class="p1">(<span class="default"><a href="hilbert2.html#K1" target="_self">prop</a> <font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 3 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font> )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a>, <a class="ref" href="finseq_1.html#T58">FINSEQ_1:58</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_1"/>
2 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font>
 ;<br/><a NAME="E2:33_1"/><b>then </b>
2 <a href="xcmplx_0.html#K2">+</a> 0 <a href="hidden.html#R1">=</a> 2 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E3:33_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:33"/>
<font color="Maroon">p</font> <a href="hilbert1.html#K4">'&amp;'</a> <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="hilbert2.html#K1" target="_self">prop</a> <font color="Maroon">n</font>
 <b>by </b><i/>;<br/>


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