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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: RFUNCT_2:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> holds  <span class="p1">(<span class="default"><a href="partfun2.html#K1" title="PARTFUN2:func.1">id</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">R</font> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a> </div></div>
