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



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:53_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a> 
 ;<br/><a NAME="E2:53_1"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hilbert1.html#K3" target="_self">=&gt;</a> <font color="Maroon">c<sub>2</sub></font> <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/><b>hence </b><a NAME="E3:53_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <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#E1:53_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="hilbert1.html#D10" target="_self">Def10</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:53"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="hilbert1.html#K6" target="_self">HP_TAUT</a>  )
 ;<br/>

<a NAME="E3:53"/>
<font color="Maroon">c<sub>1</sub></font> <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#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</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="E4:53"/><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"><font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K4" target="_self">'&amp;'</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="txt" href="hilbert1.html#E2:53"><i><font color="Green">E37</font></i></a>, <a class="ref" href="hilbert1.html#D10" target="_self">Def10</a></i>;<br/>
<b>hence </b><a NAME="E5:53"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hilbert1.html#K4" target="_self">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font> <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#E2:53"><i><font color="Green">E37</font></i></a>, <a class="ref" href="hilbert1.html#D10" target="_self">Def10</a></i>;<br/>


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