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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: QC_LANG1:12</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">F</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> holds <br/> ( ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">@</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <font color="Olive" title="b2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K12" title="QC_LANG1:func.12">VERUM</a> <font color="Olive" title="b1">A</font> ) &amp; ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">@</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies <font color="Olive" title="b2">F</font> is  <a href="qc_lang1.html#V3" title="QC_LANG1:attr.3">negative</a>  ) &amp; ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">@</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 implies <font color="Olive" title="b2">F</font> is  <a href="qc_lang1.html#V4" title="QC_LANG1:attr.4">conjunctive</a>  ) &amp; ( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">@</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> <a href="xtuple_0.html#K1" title="XTUPLE_0:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 implies <font color="Olive" title="b2">F</font> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a>  ) &amp; (  ex <font color="Olive" title="b3">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <span class="p1">(<span class="default"><a href="qc_lang1.html#K11" title="QC_LANG1:func.11">@</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 is   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-pred_symbol</a> of <font color="Olive" title="b3">k</font>,<font color="Olive" title="b1">A</font> implies <font color="Olive" title="b2">F</font> is  <a href="qc_lang1.html#V2" title="QC_LANG1:attr.2">atomic</a>  ) )</div></div>
