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<div class="add">

<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><b>that </b><br/><a NAME="E1:28_1_2"/><i><font color="Green">E22</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0 &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="limfunc1.html#K4">right_open_halfline</a> 0 holds <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="prepower.html#K12">#R</a> <font color="Maroon">c<sub>1</sub></font> ) )
 <b>and </b><br/><a NAME="E2:28_1_2"/><i><font color="Green">E23</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0 &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="limfunc1.html#K4">right_open_halfline</a> 0 holds <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="prepower.html#K12">#R</a> <font color="Maroon">c<sub>1</sub></font> ) )
 ;<br/>

<a NAME="E3:28_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0 holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:28_1_2_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#K4">right_open_halfline</a> 0
 ;<br/>

<b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="prepower.html#K12">#R</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="taylor_1.html#E1:28_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="taylor_1.html#E1:28_1_2_1"><i><font color="Green">E24</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="taylor_1.html#E2:28_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="taylor_1.html#E1:28_1_2_1"><i><font color="Green">E24</font></i></a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:28_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="taylor_1.html#E1:28_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="taylor_1.html#E2:28_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="partfun1.html#T34">PARTFUN1:34</a></i>;<br/>


</div>
