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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: MSSUBFAM:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font> being   <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="b3">F</font> being   <a href="pboole.html#NM2" title="PBOOLE:NM.2">ManySortedFunction</a> of <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b2">A</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="funct_6.html#K2" title="FUNCT_6:func.2">rngs</a> <font color="Olive" title="b3">F</font> &amp; (  for <font color="Olive" title="b4">i</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b5">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b4">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">I</font> &amp; <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font> holds <br/><font color="Olive" title="b5">f</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font></span>)</span> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) holds <br/><font color="Olive" title="b2">A</font> is <a href="finset_1.html#V2" title="FINSET_1:attr.2">V39</a>()</div></div>
