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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: CQC_THE3:47</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">p</font>, <font color="Olive" title="b3">q</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b2">p</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  &amp; <font color="Olive" title="b3">q</font> is  <a href="qc_lang1.html#V6" title="QC_LANG1:attr.6">closed</a>  holds <br/>( <font color="Olive" title="b2">p</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a> <font color="Olive" title="b3">q</font> iff  <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Olive" title="b3">q</font> <a href="cqc_the3.html#R1" title="CQC_THE3:pred.1">|-</a>  <a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Olive" title="b2">p</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T43" target="_self" onmouseover="rs('cqc_the3/T43')" onmouseout="rh()">Th43</a>, <a class="ref" href="cqc_the3.html#T45" target="_self" onmouseover="rs('cqc_the3/T45')" onmouseout="rh()">Th45</a></span>;<br/></div></div>
