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<div><span class="kw">theorem </span><a NAME="T17"><span class="comment"><font color="firebrick">:: DBLSEQ_1:17</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Pseq</font> being   <a href="dblseq_1.html#V1" title="DBLSEQ_1:attr.1">P-convergent</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#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b2">Psubseq</font> being    <a href="dblseq_1.html#M1" title="DBLSEQ_1:mode.1">subsequence</a> of <font color="Olive" title="b1">Pseq</font> holds   <a href="dblseq_1.html#K1" title="DBLSEQ_1:func.1">P-lim</a> <font color="Olive" title="b2">Psubseq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dblseq_1.html#K1" title="DBLSEQ_1:func.1">P-lim</a> <font color="Olive" title="b1">Pseq</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="dblseq_1.html#E37"><span class="lab"><font color="Green" title="E16">LM114</font></span></a></span>;<br/></div></div>
