<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E31">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: QC_LANG4:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> <br/>  for <font color="Olive" title="b2">F</font>, <font color="Olive" title="b3">G</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">QC-WFF</a> <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b4">t</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Olive" title="b2">F</font></span>)</span> holds <br/> ( <font color="Olive" title="b4">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">F</font> <a href="qc_lang4.html#K3" title="QC_LANG4:func.3">-entry_points_in_subformula_tree_of</a> <font color="Olive" title="b3">G</font> iff <span class="p1">(<span class="default"><a href="qc_lang4.html#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="trees_2.html#K5" title="TREES_2:func.5">|</a> <font color="Olive" title="b4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang4.html#K2" title="QC_LANG4:func.2">tree_of_subformulae</a> <font color="Olive" title="b3">G</font> )</div></div>
