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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: QC_LANG2:31</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> holds <br/> (  <a href="qc_lang2.html#K13" title="QC_LANG2:func.13">the_left_side_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Olive" title="b3">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F</font> &amp;  <a href="qc_lang2.html#K14" title="QC_LANG2:func.14">the_right_side_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Olive" title="b3">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">G</font> &amp;  <a href="qc_lang1.html#K19" title="QC_LANG1:func.19">the_left_argument_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Olive" title="b3">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">F</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Olive" title="b3">G</font> &amp;  <a href="qc_lang1.html#K20" title="QC_LANG1:func.20">the_right_argument_of</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="qc_lang2.html#K4" title="QC_LANG2:func.4">&lt;=&gt;</a> <font color="Olive" title="b3">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">G</font> <a href="qc_lang2.html#K2" title="QC_LANG2:func.2">=&gt;</a> <font color="Olive" title="b2">F</font> )</div></div>
