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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E27">Def13</font></span>   defines <a href="cqc_sim1.html#K15" title="CQC_SIM1:func.15">SepQuadruples</a> <a onclick="hs(this)" href="javascript:()">CQC_SIM1:def 13 : <br/></a><span> 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> 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><br/>  for <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Olive" title="b1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <font color="Olive" title="b1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Olive" title="b1">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p3">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Olive" title="b1">A</font></span>)</span>,<span class="p3">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Olive" title="b1">A</font></span>)</span>)</span>)</span></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span> holds <br/> ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K15" title="CQC_SIM1:func.15">SepQuadruples</a> <font color="Olive" title="b2">p</font> iff ( <font color="Olive">b<sub>3</sub></font> <a href="cqc_sim1.html#R1" title="CQC_SIM1:pred.1">is_Sep-closed_on</a> <font color="Olive" title="b2">p</font> &amp; (  for <font color="Olive" title="b4">D</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">[:</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Olive" title="b1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <font color="Olive" title="b1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Olive" title="b1">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p3">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Olive" title="b1">A</font></span>)</span>,<span class="p3">(<span class="default"><a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Olive" title="b1">A</font></span>)</span>)</span>)</span></span><a href="zfmisc_1.html#K4" title="ZFMISC_1:func.4">:]</a></span>  st <font color="Olive" title="b4">D</font> <a href="cqc_sim1.html#R1" title="CQC_SIM1:pred.1">is_Sep-closed_on</a> <font color="Olive" title="b2">p</font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">D</font> ) ) );<br/></span></div>
