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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E48">Th65</font></span>: <a NAME="T65"><span class="comment"><font color="firebrick">:: DBLSEQ_3:65</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being   <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> holds <br/> ( ( <font color="Olive" title="b1">f</font> is  <a href="dblseq_3.html#V7" title="DBLSEQ_3:attr.7">convergent_in_cod1</a>  implies  <a href="dblseq_3.html#K7" title="DBLSEQ_3:func.7">lim_in_cod1</a> <font color="Olive" title="b1">f</font> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>  ) &amp; ( <font color="Olive" title="b1">f</font> is  <a href="dblseq_3.html#V11" title="DBLSEQ_3:attr.11">convergent_in_cod2</a>  implies  <a href="dblseq_3.html#K8" title="DBLSEQ_3:func.8">lim_in_cod2</a> <font color="Olive" title="b1">f</font> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>  ) )</div></div>
