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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th9</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: SUBSTUT2:9</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#K14" title="SUBSTUT1:func.14">ExpandSub</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b2">p</font>,<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="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="substut1.html#K2" title="SUBSTUT1:func.2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> (<font color="Olive" title="b3">x</font>,<span class="p3">(<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> <a href="sublemma.html#K14" title="SUBLEMMA:func.14">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" title="SUBSTUT2:func.1">[</a><span class="default"><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><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span></span>)</span></span>)</span></div></div>
