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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: GOEDCPUC:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Al</font> being    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> <br/>  for <font color="Olive" title="b2">Al2</font> being  <font color="Olive">b<sub>1</sub></font> <a href="qc_trans.html#V1" title="QC_TRANS:attr.1">-expanding</a>   <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</a> <br/>  for <font color="Olive" title="b3">r</font>, <font color="Olive" title="b4">s</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">Al</font><br/>  for <font color="Olive" title="b5">x</font> being   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Olive" title="b1">Al</font> holds <br/> ( <font color="Olive" title="b2">Al2</font> <a href="qc_trans.html#K1" title="QC_TRANS:func.1">-Cast</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">r</font> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <font color="Olive" title="b4">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">Al2</font> <a href="qc_trans.html#K1" title="QC_TRANS:func.1">-Cast</a> <font color="Olive" title="b3">r</font></span>)</span> <a href="cqc_lang.html#K9" title="CQC_LANG:func.9">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">Al2</font> <a href="qc_trans.html#K1" title="QC_TRANS:func.1">-Cast</a> <font color="Olive" title="b4">s</font></span>)</span> &amp; <font color="Olive" title="b2">Al2</font> <a href="qc_trans.html#K1" title="QC_TRANS:func.1">-Cast</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<font color="Olive" title="b5">x</font>,<font color="Olive" title="b3">r</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">Ex</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">Al2</font> <a href="qc_trans.html#K2" title="QC_TRANS:func.2">-Cast</a> <font color="Olive" title="b5">x</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">Al2</font> <a href="qc_trans.html#K1" title="QC_TRANS:func.1">-Cast</a> <font color="Olive" title="b3">r</font></span>)</span>) )</div></div>
