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<b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>let </b><font color="Maroon">seq'</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:19"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">seq</font> is <a href="seq_2.html#V4" target="_self">convergent</a>
 <b>and </b><br/><a NAME="E2:19"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">seq'</font> is <a href="seq_2.html#V4" target="_self">convergent</a>
 ;<br/>

<a NAME="E3:19"/><i><font color="Green">E39</font></i>: 
 <a href="seq_1.html#K17">-</a> <font color="Maroon">seq'</font> is <a href="seq_2.html#V4" target="_self">convergent</a>
 
<b>by </b><i>, </i>;<br/>
<b>thus </b> <a href="seq_2.html#K2" target="_self">lim</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K10">-</a> <font color="Maroon">seq'</font></span>)</span> = 
 <a href="seq_2.html#K2" target="_self">lim</a> <span class="p1">(<span class="default"><font color="Maroon">seq</font> <a href="seq_1.html#K9">+</a> <span class="p2">(<span class="default"><a href="seq_1.html#K17">-</a> <font color="Maroon">seq'</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T15">SEQ_1:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="seq_2.html#K2" target="_self">lim</a> <font color="Maroon">seq</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="seq_2.html#K2" target="_self">lim</a> <span class="p2">(<span class="default"><a href="seq_1.html#K17">-</a> <font color="Maroon">seq'</font></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="seq_2.html#K2" target="_self">lim</a> <font color="Maroon">seq</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> <span class="p2">(<span class="default"><a href="seq_2.html#K2" target="_self">lim</a> <font color="Maroon">seq'</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="seq_2.html#K2" target="_self">lim</a> <font color="Maroon">seq</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="seq_2.html#K2" target="_self">lim</a> <font color="Maroon">seq'</font></span>)</span>

;<br/>


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