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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th34</font></span>: <a NAME="T34"><span class="comment"><font color="firebrick">:: CQC_SIM1:34</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">t</font> being   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">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><br/>  for <font color="Olive" title="b5">f</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<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="p1">(<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>)<br/>  for <font color="Olive" title="b6">K</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <span class="p1">(<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>  holds <br/>(  not <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Olive" title="b4">q</font>,<font color="Olive" title="b2">t</font>,<font color="Olive" title="b6">K</font>,<font color="Olive" title="b5">f</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_sim1.html#K15" title="CQC_SIM1:func.15">SepQuadruples</a> <font color="Olive" title="b3">p</font> or <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Olive" title="b4">q</font>,<font color="Olive" title="b2">t</font>,<font color="Olive" title="b6">K</font>,<font color="Olive" title="b5">f</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Olive" title="b3">p</font>,<span class="p2">(<span class="default"><a href="cqc_sim1.html#K13" title="CQC_SIM1:func.13">index</a> <font color="Olive" title="b3">p</font></span>)</span>,<span class="p2">(<span class="default"><a href="setwiseo.html#K1" title="SETWISEO:func.1">{}.</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="cqc_sim1.html#K11" title="CQC_SIM1:func.11">id</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><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> or <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K6" title="CQC_LANG:func.6">'not'</a> <font color="Olive" title="b4">q</font></span>)</span>,<font color="Olive" title="b2">t</font>,<font color="Olive" title="b6">K</font>,<font color="Olive" title="b5">f</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_sim1.html#K15" title="CQC_SIM1:func.15">SepQuadruples</a> <font color="Olive" title="b3">p</font> or  ex <font color="Olive" title="b7">r</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 <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">q</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b7">r</font></span>)</span>,<font color="Olive" title="b2">t</font>,<font color="Olive" title="b6">K</font>,<font color="Olive" title="b5">f</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_sim1.html#K15" title="CQC_SIM1:func.15">SepQuadruples</a> <font color="Olive" title="b3">p</font> or  ex <font color="Olive" title="b7">r</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> ex <font color="Olive" title="b8">u</font> being   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Olive" title="b1">A</font> st <br/>( <font color="Olive" title="b2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">u</font> <a href="qc_lang1.html#K30" title="QC_LANG1:func.30">+</a> <span class="p1">(<span class="default"><a href="cqc_sim1.html#K7" title="CQC_SIM1:func.7">QuantNbr</a> <font color="Olive" title="b7">r</font></span>)</span> &amp; <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b7">r</font> <a href="cqc_lang.html#K7" title="CQC_LANG:func.7">'&amp;'</a> <font color="Olive" title="b4">q</font></span>)</span>,<font color="Olive" title="b8">u</font>,<font color="Olive" title="b6">K</font>,<font color="Olive" title="b5">f</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_sim1.html#K15" title="CQC_SIM1:func.15">SepQuadruples</a> <font color="Olive" title="b3">p</font> ) or  ex <font color="Olive" title="b7">x</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="qc_lang1.html#K3" title="QC_LANG1:func.3">bound_QC-variables</a> <font color="Olive" title="b1">A</font> ex <font color="Olive" title="b8">u</font> being   <a href="qc_lang1.html#NM2" title="QC_LANG1:NM.2">QC-symbol</a> of <font color="Olive" title="b1">A</font> ex <font color="Olive" title="b9">h</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<span class="p1">(<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="p1">(<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>) st <br/>( <font color="Olive" title="b8">u</font> <a href="qc_lang1.html#K28" title="QC_LANG1:func.28">++</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t</font> &amp; <font color="Olive" title="b9">h</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b7">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<span class="default"><a href="qc_lang3.html#K2" title="QC_LANG3:func.2">x.</a> <font color="Olive" title="b8">u</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">f</font> &amp; ( <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b7">x</font>,<font color="Olive" title="b4">q</font>)</span>)</span>,<font color="Olive" title="b8">u</font>,<font color="Olive" title="b6">K</font>,<font color="Olive" title="b9">h</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_sim1.html#K15" title="CQC_SIM1:func.15">SepQuadruples</a> <font color="Olive" title="b3">p</font> or <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b7">x</font>,<font color="Olive" title="b4">q</font>)</span>)</span>,<font color="Olive" title="b8">u</font>,<span class="p2">(<span class="default"><font color="Olive" title="b6">K</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b7">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>,<font color="Olive" title="b9">h</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="cqc_sim1.html#K15" title="CQC_SIM1:func.15">SepQuadruples</a> <font color="Olive" title="b3">p</font> ) ) )</div></div>
