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<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/>



<b>consider </b><font color="Maroon">p'</font> being   <a href="trees_2.html#NM6">DecoratedTree</a> of  <a href="hilbert1.html#K1">HP-WFF</a> , <font color="Maroon">q'</font> being   <a href="trees_2.html#NM6">DecoratedTree</a> of  <a href="hilbert1.html#K1">HP-WFF</a> <b> such that </b><br/><a NAME="E2:44"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">p'</font> <a href="hidden.html#R1">=</a> <a href="hilbert2.html#K2" target="_self">HP-Subformulae</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> &amp; <font color="Maroon">q'</font> <a href="hidden.html#R1">=</a> <a href="hilbert2.html#K2" target="_self">HP-Subformulae</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">q</font> )
 <b>and </b><br/><a NAME="E3:44"/>
<a href="hilbert2.html#K2" target="_self">HP-Subformulae</a>  <a href="funct_1.html#K1">.</a> <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="hidden.html#R1">=</a> <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="trees_4.html#K10">-tree</a> <font color="Maroon">p'</font>,<font color="Maroon">q'</font>
 <b>and </b><br/><a NAME="E4:44"/><i><font color="Green">E30</font></i>: 
<a href="hilbert2.html#K2" target="_self">HP-Subformulae</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="trees_4.html#K10">-tree</a> <font color="Maroon">p'</font>,<font color="Maroon">q'</font>
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E5:44"/>
 <a href="hilbert2.html#K3" target="_self">Subformulae</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="hilbert1.html#K3">=&gt;</a> <font color="Maroon">q</font></span>)</span> <a href="trees_4.html#K10">-tree</a> <span class="p1">(<span class="default"><a href="hilbert2.html#K3" target="_self">Subformulae</a> <font color="Maroon">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="hilbert2.html#K3" target="_self">Subformulae</a> <font color="Maroon">q</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


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