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<div><span class="kw">theorem </span><a NAME="T13"><span class="comment"><font color="firebrick">:: DBLSEQ_1:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Rseq</font> being   <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#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b2">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">Rseq</font> is  <a href="dblseq_1.html#V1" title="DBLSEQ_1:attr.1">P-convergent</a>  holds <br/>( <font color="Olive" title="b2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b1">Rseq</font> is  <a href="dblseq_1.html#V1" title="DBLSEQ_1:attr.1">P-convergent</a>  &amp;  <a href="dblseq_1.html#K1" title="DBLSEQ_1:func.1">P-lim</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b1">Rseq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">r</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="dblseq_1.html#K1" title="DBLSEQ_1:func.1">P-lim</a> <font color="Olive" title="b1">Rseq</font></span>)</span> )</div></div>
