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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th3</font></span>: <a NAME="T4"><span class="comment"><font color="firebrick">:: CARDFIL3:4</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font>, <font color="Olive" title="b2">X</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  <font color="Olive">b<sub>2</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">q</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b1">I</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b4">p</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b5">q</font></span>)</span> <a href="relat_1.html#NK6" title="RELAT_1:NK.6">*</a> <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">p</font> <a href="relat_1.html#NK6" title="RELAT_1:NK.6">*</a> <font color="Olive" title="b3">x</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">q</font> <a href="relat_1.html#NK6" title="RELAT_1:NK.6">*</a> <font color="Olive" title="b3">x</font></span>)</span></div></div>
