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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th51</font></span>: <a NAME="T51"><span class="comment"><font color="firebrick">:: RFUNCT_1:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</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="b2">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b1">C</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> holds <br/> ( <font color="Olive" title="b3">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  iff <font color="Olive" title="b2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b3">f</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  ) <span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D5" onmouseover="rs('valued_1/D5')" onmouseout="rh()">VALUED_1:def 5</a></span>;<br/></div></div>
