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<div><span class="kw">theorem </span><a NAME="T50"><span class="comment"><font color="firebrick">:: RFUNCT_2:50</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">g</font>, <font color="Olive" title="b2">p</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b3">h</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st ( <font color="Olive" title="b3">h</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">g</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a>  or <font color="Olive" title="b3">h</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">g</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> is  <a href="valued_0.html#V6" title="VALUED_0:attr.6">decreasing</a>  ) holds <br/><font color="Olive" title="b3">h</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">g</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> </div></div>
