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<div><span class="kw">theorem </span><a NAME="T13"><span class="comment"><font color="firebrick">:: VALUAT_1:13</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">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="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">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="b5">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="b2">A</font> holds   <a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<span class="p1">(<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="b4">p</font>)</span>)</span>,<font color="Olive" title="b5">J</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="valuat_1.html#K3" title="VALUAT_1:func.3">FOR_ALL</a> (<font color="Olive" title="b3">x</font>,<span class="p1">(<span class="default"><a href="valuat_1.html#K8" title="VALUAT_1:func.8">Valid</a> (<font color="Olive" title="b4">p</font>,<font color="Olive" title="b5">J</font>)</span>)</span>) <span class="kw">by</span> <span class="lab"><a class="txt" href="valuat_1.html#E10"><span class="lab"><font color="Green" title="E8">Lm1</font></span></a></span>;<br/></div></div>
