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<div><span class="kw">theorem </span><a NAME="T85"><span class="comment"><font color="firebrick">:: LIMFUNC1:85</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>  st <font color="Olive" title="b1">f</font> is  <a href="limfunc1.html#V3" title="LIMFUNC1:attr.3">convergent_in+infty</a>  holds <br/>(  <a href="valued_1.html#K56" title="VALUED_1:func.56">abs</a> <font color="Olive" title="b1">f</font> is  <a href="limfunc1.html#V3" title="LIMFUNC1:attr.3">convergent_in+infty</a>  &amp;  <a href="limfunc1.html#K4" title="LIMFUNC1:func.4">lim_in+infty</a> <span class="p1">(<span class="default"><a href="valued_1.html#K56" title="VALUED_1:func.56">abs</a> <font color="Olive" title="b1">f</font></span>)</span> <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="limfunc1.html#K4" title="LIMFUNC1:func.4">lim_in+infty</a> <font color="Olive" title="b1">f</font></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> )</div></div>
