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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/>





<b>assume </b><a NAME="E1:63"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="limfunc2.html#R4" target="_self">is_right_convergent_in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="limfunc2.html#R4" target="_self">is_right_convergent_in</a> <font color="Maroon">c<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K7">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> ) ) )
 ;<br/>

<a NAME="E2:63"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K7">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K6">+</a> <span class="p1">(<span class="default"><a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T40">RFUNCT_1:40</a></i>;<br/>
<a NAME="E3:63"/><i><font color="Green">E38</font></i>: 
 <a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="limfunc2.html#R4" target="_self">is_right_convergent_in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="limfunc2.html#E1:63"><i><font color="Green">E36</font></i></a>, <a class="ref" href="limfunc2.html#T61" target="_self">Th61</a></i>;<br/>
<b>hence </b><a NAME="E4:63"/>
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K7">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="limfunc2.html#R4" target="_self">is_right_convergent_in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="limfunc2.html#E1:63"><i><font color="Green">E36</font></i></a>, <a class="txt" href="limfunc2.html#E2:63"><i><font color="Green">E37</font></i></a>, <a class="ref" href="limfunc2.html#T62" target="_self">Th62</a></i>;<br/>

<b>thus </b> <a href="limfunc2.html#K2" target="_self">lim_right</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K7">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><a href="limfunc2.html#K2" target="_self">lim_right</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="limfunc2.html#K2" target="_self">lim_right</a> <span class="p2">(<span class="default"><a href="seq_1.html#K16">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="limfunc2.html#E1:63"><i><font color="Green">E36</font></i></a>, <a class="txt" href="limfunc2.html#E2:63"><i><font color="Green">E37</font></i></a>, <a class="txt" href="limfunc2.html#E3:63"><i><font color="Green">E38</font></i></a>, <a class="ref" href="limfunc2.html#T62" target="_self">Th62</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="limfunc2.html#K2" target="_self">lim_right</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></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="limfunc2.html#K2" target="_self">lim_right</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="limfunc2.html#E1:63"><i><font color="Green">E36</font></i></a>, <a class="ref" href="limfunc2.html#T61" target="_self">Th61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="limfunc2.html#K2" target="_self">lim_right</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="limfunc2.html#K2" target="_self">lim_right</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>

;<br/>


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