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<div><span class="kw">theorem </span><a NAME="T48"><span class="comment"><font color="firebrick">:: LIMFUNC2:48</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x0</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b2">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>  st <font color="Olive" title="b2">f</font> <a href="limfunc2.html#R1" title="LIMFUNC2:pred.1">is_left_convergent_in</a> <font color="Olive" title="b1">x0</font> holds <br/>(  <a href="valued_1.html#K56" title="VALUED_1:func.56">abs</a> <font color="Olive" title="b2">f</font> <a href="limfunc2.html#R1" title="LIMFUNC2:pred.1">is_left_convergent_in</a> <font color="Olive" title="b1">x0</font> &amp;  <a href="limfunc2.html#K1" title="LIMFUNC2:func.1">lim_left</a> (<span class="p1">(<span class="default"><a href="valued_1.html#K56" title="VALUED_1:func.56">abs</a> <font color="Olive" title="b2">f</font></span>)</span>,<font color="Olive" title="b1">x0</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><a href="limfunc2.html#K1" title="LIMFUNC2:func.1">lim_left</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">x0</font>)</span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> )</div></div>
