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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E72">Th70</font></span>: <a NAME="T70"><span class="comment"><font color="firebrick">:: PREPOWER:70</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font> being   <a href="prepower.html#NM1" title="PREPOWER:NM.1">Rational_Sequence</a><br/>  for <font color="Olive" title="b3">a</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">s1</font> is  <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  &amp; <font color="Olive" title="b2">s2</font> is  <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  &amp;  <a href="seq_2.html#K1" title="SEQ_2:func.1">lim</a> <font color="Olive" title="b1">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_2.html#K1" title="SEQ_2:func.1">lim</a> <font color="Olive" title="b2">s2</font> &amp; <font color="Olive" title="b3">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/>( <font color="Olive" title="b3">a</font> <a href="prepower.html#K5" title="PREPOWER:func.5">#Q</a> <font color="Olive" title="b1">s1</font> is  <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  &amp; <font color="Olive" title="b3">a</font> <a href="prepower.html#K5" title="PREPOWER:func.5">#Q</a> <font color="Olive" title="b2">s2</font> is  <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  &amp;  <a href="seq_2.html#K1" title="SEQ_2:func.1">lim</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="prepower.html#K5" title="PREPOWER:func.5">#Q</a> <font color="Olive" title="b1">s1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_2.html#K1" title="SEQ_2:func.1">lim</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="prepower.html#K5" title="PREPOWER:func.5">#Q</a> <font color="Olive" title="b2">s2</font></span>)</span> )</div></div>
