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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E31">Th24</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: CALCUL_1:24</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>, <font color="Olive" title="b4">y</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="b5">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b6">J</font> being    <a href="valuat_1.html#M1" title="VALUAT_1:mode.1">interpretation</a> of <font color="Olive" title="b1">Al</font>,<font color="Olive" title="b5">A</font><br/>  for <font color="Olive" title="b7">v</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="valuat_1.html#K2" title="VALUAT_1:func.2">Valuations_in</a> (<font color="Olive" title="b1">Al</font>,<font color="Olive" title="b5">A</font>) holds <br/> ( <font color="Olive" title="b6">J</font>,<font color="Olive" title="b7">v</font> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Olive" title="b2">p</font> <a href="substut2.html#K4" title="SUBSTUT2:func.4">.</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>) iff  ex <font color="Olive" title="b8">a</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b5">A</font> st <br/>( <font color="Olive" title="b7">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b8">a</font> &amp; <font color="Olive" title="b6">J</font>,<font color="Olive" title="b7">v</font> <a href="sublemma.html#K1" title="SUBLEMMA:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">x</font> <a href="sublemma.html#K12" title="SUBLEMMA:func.12">|</a> <font color="Olive" title="b8">a</font></span>)</span> <a href="valuat_1.html#R1" title="VALUAT_1:pred.1">|=</a> <font color="Olive" title="b2">p</font> ) )</div></div>
