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<a NAME="E1:1_1_1"/><i><font color="Green">E1</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#NR1" target="_self">is_not_0</a>  &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="fdiff_1.html#D1">FDIFF_1:def 1</a></i>;<br/>
<a NAME="E2:1_1_1"/><b>then </b><i><font color="Green">E2</font></i>: 
 <a href="seq_1.html#K17">-</a> <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#NR1" target="_self">is_not_0</a> 
 
<b>by </b><i><a class="ref" href="seq_1.html#T53">SEQ_1:53</a></i>;<br/>
<a NAME="E3:1_1_1"/><i><font color="Green">E3</font></i>: 
 <a href="seq_1.html#K17">-</a> <font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V4">convergent</a>
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:1_1_1"><i><font color="Green">E1</font></i></a>, <a class="ref" href="seq_2.html#T23">SEQ_2:23</a></i>;<br/>
<a NAME="E4:1_1_1"/>
 <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="seq_1.html#K17">-</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 0
 
<b>by </b><i><a class="txt" href="fdiff_2.html#E1:1_1_1"><i><font color="Green">E1</font></i></a>, <a class="ref" href="seq_2.html#T24">SEQ_2:24</a></i>;<br/>
<b>hence </b><a NAME="E5:1_1_1"/>
 <a href="seq_1.html#K15">-</a> <font color="Maroon">c<sub>1</sub></font> is  <a href="fdiff_1.html#V1">convergent_to_0</a> <a href="seq_1.html#NM1">Real_Sequence</a>
 <b>by </b><i><a class="txt" href="fdiff_2.html#E2:1_1_1"><i><font color="Green">E2</font></i></a>, <a class="txt" href="fdiff_2.html#E3:1_1_1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="fdiff_1.html#D1">FDIFF_1:def 1</a></i>;<br/>


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