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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th36</font></span>: <a NAME="T36"><span class="comment"><font color="firebrick">:: QC_LANG3:36</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> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="qc_lang1.html#K9" title="QC_LANG1:func.9">QC-WFF</a> <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">V</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="qc_lang1.html#K2" title="QC_LANG1:func.2">QC-variables</a> <font color="Olive" title="b1">A</font></span>)</span>  st <font color="Olive" title="b2">p</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  holds <br/>(  <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">V</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang3.html#K1" title="QC_LANG3:func.1">variables_in</a> (<span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_arguments_of</a> <font color="Olive" title="b2">p</font></span>)</span>,<font color="Olive" title="b3">V</font>) &amp;  <a href="qc_lang3.html#K4" title="QC_LANG3:func.4">Vars</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">V</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_arguments_of</a> <font color="Olive" title="b2">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">k</font></span>)</span> where <font color="Olive" title="b4">k</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">k</font> &amp; <font color="Olive" title="b4">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_arguments_of</a> <font color="Olive" title="b2">p</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" title="QC_LANG1:func.17">the_arguments_of</a> <font color="Olive" title="b2">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">V</font> ) </span> } </span>  )</div></div>
