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<div><span class="kw">theorem </span><a NAME="T2"><span class="comment"><font color="firebrick">:: CATALG_1:2</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>, <font color="Olive" title="b3">B</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="b4">f</font>, <font color="Olive" title="b5">g</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st  <a href="funct_6.html#K2" title="FUNCT_6:func.2">rngs</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> (<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">A</font>)</span>)</span> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Olive" title="b3">B</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b5">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> (<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">g</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> (<font color="Olive" title="b1">I</font>,<font color="Olive" title="b3">B</font>)</span>)</span> <a href="pboole.html#K8" title="PBOOLE:func.8">**</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">f</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> (<font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">A</font>)</span>)</span></div></div>
