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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: SUBLEMMA:31</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">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><br/>  for <font color="Olive" title="b3">S</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Olive" title="b1">Al</font><br/>  for <font color="Olive" title="b4">xSQ</font> being    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Olive" title="b3">S</font>,<font color="Olive" title="b2">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span>  st <span class="p1"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Olive" title="b3">S</font>,<font color="Olive" title="b2">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  holds <br/> <a href="sublemma.html#K11" title="SUBLEMMA:func.11">CQCQuant</a> (<span class="p1">(<span class="default"><a href="sublemma.html#K9" title="SUBLEMMA:func.9">CQCSub_All</a> (<span class="p2"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Olive" title="b3">S</font>,<font color="Olive" title="b2">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span>,<font color="Olive" title="b4">xSQ</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <font color="Olive" title="b3">S</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<span class="p1">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p2">(<span class="default"><a href="substut1.html#K32" title="SUBSTUT1:func.32">@</a> <span class="p3">(<span class="default"><a href="sublemma.html#K9" title="SUBLEMMA:func.9">CQCSub_All</a> (<span class="p4"><a href="sublemma.html#K7" title="SUBLEMMA:func.7">[</a><span class="default"><font color="Olive" title="b3">S</font>,<font color="Olive" title="b2">x</font></span><a href="sublemma.html#K7" title="SUBLEMMA:func.7">]</a></span>,<font color="Olive" title="b4">xSQ</font>)</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K39" title="SUBSTUT1:func.39">CQC_Sub</a> <font color="Olive" title="b3">S</font></span>)</span>)</div></div>
