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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <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" target="_self">HP-WFF</a> ;<br/>





<a NAME="E1:48"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a> 
 
<b>by </b><i><a class="ref" href="hilbert1.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E2:48"/><b>then </b><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></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">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a> 
 
<b>by </b><i><a class="ref" href="hilbert1.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E3:48"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></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">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a> 
 
<b>by </b><i><a class="ref" href="hilbert1.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E4:48"/><b>then </b><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a> 
 
<b>by </b><i><a class="txt" href="hilbert1.html#E2:48"><i><font color="Green">E33</font></i></a>, <a class="ref" href="hilbert1.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E5:48"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a> 
 
<b>by </b><i><a class="ref" href="hilbert1.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E6:48"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a> 
 
<b>by </b><i><a class="txt" href="hilbert1.html#E4:48"><i><font color="Green">E34</font></i></a>, <a class="ref" href="hilbert1.html#D10" target="_self">Def10</a></i>;<br/>
<b>hence </b><a NAME="E7:48"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a> 
 <b>by </b><i><a class="ref" href="hilbert1.html#T20" target="_self">Th20</a></i>;<br/>


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