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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="hilbert1.html#K1">HP-WFF</a> ;<br/>





<i><font color="Green">E28</font></i>: <font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>3</sub></font>

<br/>.= 
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</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">c<sub>2</sub></font> <a href="finseq_1.html#K7">^</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
;<br/>
<a NAME="E2:35"/><i><font color="Green">E29</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 1 &amp; <span class="p1">(<span class="default"><a href="hilbert2.html#K1" target="_self">prop</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 3 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="hilbert2.html#E1:35"><i><font color="Green">E28</font></i></a>, <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="35_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:35_2"/>
1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:35_2"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 0 <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><b>hence </b><a NAME="E3:35_2"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:35"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="hilbert2.html#K1" target="_self">prop</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="hilbert2.html#E2:35"><i><font color="Green">E29</font></i></a></i>;<br/>


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