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<div><span class="kw">theorem </span><a NAME="T22"><span class="comment"><font color="firebrick">:: SUBLEMMA:22</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">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="b2">A</font>)<br/>  for <font color="Olive" title="b4">S1</font>, <font color="Olive" title="b5">S2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-Sub-WFF</a> <font color="Olive" title="b1">Al</font>  st <font color="Olive" title="b4">S1</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">S2</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  holds <br/>(  <a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">S1</font>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b3">v</font>,<span class="p1">(<span class="default"><a href="sublemma.html#K6" title="SUBLEMMA:func.6">CQCSub_&amp;</a> (<font color="Olive" title="b4">S1</font>,<font color="Olive" title="b5">S2</font>)</span>)</span>) &amp;  <a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b3">v</font>,<font color="Olive" title="b5">S2</font>) <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="sublemma.html#K3" title="SUBLEMMA:func.3">Val_S</a> (<font color="Olive" title="b3">v</font>,<span class="p1">(<span class="default"><a href="sublemma.html#K6" title="SUBLEMMA:func.6">CQCSub_&amp;</a> (<font color="Olive" title="b4">S1</font>,<font color="Olive" title="b5">S2</font>)</span>)</span>) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="sublemma.html#T21" target="_self" onmouseover="rs('sublemma/T21')" onmouseout="rh()">Th21</a></span>;<br/></div></div>
