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<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="hilbert1.html#K1" title="HILBERT1:func.1">HP-WFF</a> ;<br/>



<b>consider </b><font color="Maroon" title="c3">p'</font>, <font color="Maroon" title="c4">q'</font> being   <a href="trees_2.html#NM6" title="TREES_2:NM.6">DecoratedTree</a> of  <a href="hilbert1.html#K1" title="HILBERT1:func.1">HP-WFF</a> <b> such that </b><br/><a NAME="E2:43"/><i><font color="Green" title="E34">A1</font></i>: 
( <font color="Maroon" title="c3">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="hilbert2.html#K2" title="HILBERT2:func.2">HP-Subformulae</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">p</font> &amp; <font color="Maroon" title="c4">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="hilbert2.html#K2" title="HILBERT2:func.2">HP-Subformulae</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">q</font> &amp; <a href="hilbert2.html#K2" title="HILBERT2:func.2">HP-Subformulae</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="trees_4.html#K10" title="TREES_4:func.10">-tree</a> <font color="Maroon" title="c3">p'</font>,<font color="Maroon" title="c4">q'</font> )
 <b>and </b><br/><a NAME="E3:43"/>
<a href="hilbert2.html#K2" title="HILBERT2:func.2">HP-Subformulae</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="trees_4.html#K10" title="TREES_4:func.10">-tree</a> <font color="Maroon" title="c3">p'</font>,<font color="Maroon" title="c4">q'</font>
 <b>by </b><i><a class="ref" href="hilbert2.html#D9" target="_self" title="HILBERT2:def.9">Def9</a></i>;<br/>
<b>thus </b><a NAME="E4:43"/>
 <a href="hilbert2.html#K3" title="HILBERT2:func.3">Subformulae</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="hilbert1.html#K4" title="HILBERT1:func.4">'&amp;'</a> <font color="Maroon" title="c2">q</font></span>)</span> <a href="trees_4.html#K10" title="TREES_4:func.10">-tree</a> <span class="p1">(<span class="default"><a href="hilbert2.html#K3" title="HILBERT2:func.3">Subformulae</a> <font color="Maroon" title="c1">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="hilbert2.html#K3" title="HILBERT2:func.3">Subformulae</a> <font color="Maroon" title="c2">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="hilbert2.html#E2:43"><i><font color="Green" title="E34">A1</font></i></a></i>;<br/>


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