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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th6</font></span>: <a NAME="T4"><span class="comment"><font color="firebrick">:: MESFUN15:4</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</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><br/>  for <font color="Olive" title="b2">a</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">f</font> <a href="limfunc2.html#R1" title="LIMFUNC2:pred.1">is_left_convergent_in</a> <font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b1">f</font> is  <a href="valued_0.html#V9" title="VALUED_0:attr.9">non-decreasing</a>  holds <br/> for <font color="Olive" title="b3">x</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b3">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">a</font> holds <br/><font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="limfunc2.html#K1" title="LIMFUNC2:func.1">lim_left</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">a</font>)</div></div>
