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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E82">Th83</font></span>: <a NAME="T83"><span class="comment"><font color="firebrick">:: SUBLEMMA:83</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">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">Al</font><br/>  for <font color="Olive" title="b3">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="b4">Sub</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a> of <font color="Olive" title="b1">Al</font> holds   <a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Olive" title="b3">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b2">p</font>)</span>)</span>,<font color="Olive" title="b4">Sub</font>)</span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <font color="Olive" title="b4">Sub</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <font color="Olive" title="b4">Sub</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p3">(<span class="default"><a href="sublemma.html#K15" title="SUBLEMMA:func.15">RSub1</a> <span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b2">p</font>)</span>)</span></span>)</span></span>)</span> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <font color="Olive" title="b4">Sub</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p3">(<span class="default"><a href="sublemma.html#K16" title="SUBLEMMA:func.16">RSub2</a> (<span class="p4">(<span class="default"><a href="cqc_lang.html#K11" title="CQC_LANG:func.11">All</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b2">p</font>)</span>)</span>,<font color="Olive" title="b4">Sub</font>)</span>)</span></span>)</span></span>)</span></div></div>
