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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th9</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: FCONT_3:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">f</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <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="b2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="partfun2.html#K2" title="PARTFUN2:func.2">"</a></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b1">X</font></span>)</span> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">increasing</a> </div></div>
