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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="toprns_1.html#NM1">Real_Sequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:52"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="toprns_1.html#V3" target="_self">convergent</a>
 ;<br/>

<a NAME="E2:52"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="toprns_1.html#K2" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> is <a href="toprns_1.html#V3" target="_self">convergent</a>
 
<b>by </b><i><a class="ref" href="toprns_1.html#T43" target="_self">Th43</a></i>;<br/>
<b>hence </b><a NAME="E3:52"/>
 <a href="toprns_1.html#K3" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font> is <a href="toprns_1.html#V3" target="_self">convergent</a>
 <b>by </b><i><a class="ref" href="toprns_1.html#T12" target="_self">Th12</a></i>;<br/>


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