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<b>let </b><font color="Maroon">F</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> ;<br/><b>let </b><font color="Maroon">t</font> be    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span>;<br/>



<b>set </b><font color="Maroon">G</font> = <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">t</font>;<br/>
<b>assume </b><a NAME="E1:56"/><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">t</font> is <a href="qc_lang1.html#V5">universal</a>
 ;<br/>

<b>consider </b><font color="Maroon">H</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8">QC-WFF</a> <b> such that </b><br/><a NAME="E3:56"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K21">the_scope_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">t</font></span>)</span>
 ;<br/>
<a NAME="E4:56"/>
<font color="Maroon">H</font> <a href="qc_lang2.html#R1">is_immediate_constituent_of</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">t</font>
 
<b>by </b><i><a class="ref" href="qc_lang4.html#T8" target="_self">Th8</a>, , <a class="ref" href="qc_lang2.html#T67">QC_LANG2:67</a></i>;<br/>
<b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:56"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">t</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">m</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> &amp; <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">m</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">t'</font> being    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span><b> such that </b><br/><a NAME="E8:56"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">t'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">m</font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="qc_lang4.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E9:56"/>
( <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">t'</font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K21">the_scope_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">t</font></span>)</span> &amp; <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="qc_lang4.html#T8" target="_self">Th8</a>, <a class="ref" href="qc_lang4.html#T10" target="_self">Th10</a>, </i>;<br/>
<b>hence </b><a NAME="E10:56"/>
( <font color="Maroon">t</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K21">the_scope_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang4.html#K2" target="_self">tree_of_subformulae</a> <font color="Maroon">F</font></span>)</span> <a href="trees_2.html#K3">.</a> <font color="Maroon">t</font></span>)</span> )
 <b>by </b><i><a class="ref" href="qc_lang4.html#T10" target="_self">Th10</a></i>;<br/>


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