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<div><span class="kw">theorem </span><a NAME="T3"><span class="comment"><font color="firebrick">:: CATALG_1:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b2">I</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">B</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b2">I</font>  st (  for <font color="Olive" title="b5">i</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b5">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">I</font> holds <br/>( <font color="Olive" title="b3">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b1">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">.:</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> ) ) holds <br/><font color="Olive" title="b1">f</font> <a href="catalg_1.html#K1" title="CATALG_1:func.1">-MSF</a> (<font color="Olive" title="b2">I</font>,<font color="Olive" title="b3">A</font>) is    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Olive" title="b3">A</font>,<font color="Olive" title="b4">B</font></div></div>
