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<b>consider </b><font color="Maroon" title="c3">s</font> being   <a href="prepower.html#NM1" title="PREPOWER:NM.1">Rational_Sequence</a><b> such that </b><br/><a NAME="E2:93_1_1"/><i><font color="Green" title="E75">A2</font></i>: 
( <font color="Maroon" title="c3">s</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> &amp; ( for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c3">s</font> <a href="prepower.html#K10" title="PREPOWER:func.10">.</a> <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font> ) )
 <b>by </b><i><a class="ref" href="prepower.html#T79" target="_self" title="PREPOWER:th.79">Th79</a></i>;<br/>
<a NAME="E3:93_1_1"/><i><font color="Green" title="E76">A3</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c3">s</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 
<b>by </b><i><a class="txt" href="prepower.html#E1:93"><i><font color="Green" title="E74">A1</font></i></a>, <a class="txt" href="prepower.html#E2:93_1_1"><i><font color="Green" title="E75">A2</font></i></a>, <a class="ref" href="prepower.html#T82" target="_self" title="PREPOWER:th.82">Th82</a></i>;<br/>
<b>take </b>
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c3">s</font></span>)</span>
;<br/>

<b>thus </b><a NAME="E4:93_1_1"/>
 ex <font color="Olive" title="b1">s</font> being  <a href="prepower.html#NM1" title="PREPOWER:NM.1">Rational_Sequence</a> st <br/>( <font color="Olive" title="b1">s</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c1">a</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Olive" title="b1">s</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="prepower.html#K11" title="PREPOWER:func.11">#Q</a> <font color="Maroon" title="c3">s</font></span>)</span> )
 <b>by </b><i><a class="txt" href="prepower.html#E2:93_1_1"><i><font color="Green" title="E75">A2</font></i></a>, <a class="txt" href="prepower.html#E3:93_1_1"><i><font color="Green" title="E76">A3</font></i></a></i>;<br/>


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