<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K10" target="_self">In_Power</a> 0;<br/>
<i><font color="Green">E25</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K10" target="_self">In_Power</a> 0</span>)</span> = 
0 <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="newton.html#D4" target="_self">Def4</a></i>
<br/>.= 
1

;<br/>
<a NAME="E2:43"/><b>then </b><i><font color="Green">E26</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K10" target="_self">In_Power</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:43"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K10" target="_self">In_Power</a> 0</span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:43"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K10" target="_self">In_Power</a> 0</span>)</span>
 ;<br/>
<a NAME="E6:43"/><i><font color="Green">E28</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K10" target="_self">In_Power</a> 0</span>)</span>
 
<b>by </b><i><a class="txt" href="newton.html#E2:43"><i><font color="Green">E26</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="newton.html#E5:43"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E8:43"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="newton.html#E2:43"><i><font color="Green">E26</font></i></a>, <a class="txt" href="newton.html#E5:43"><i><font color="Green">E27</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = 0 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>6</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="newton.html#E8:43"><i><font color="Green">E29</font></i></a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K10" target="_self">In_Power</a> 0</span>)</span> <a href="seq_1.html#K2">.</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">0 <a href="newton.html#K9" target="_self">choose</a> 0</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K2" target="_self">|^</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2" target="_self">|^</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="newton.html#E6:43"><i><font color="Green">E28</font></i></a>, <a class="txt" href="newton.html#E8:43"><i><font color="Green">E29</font></i></a>, <a class="ref" href="newton.html#D4" target="_self">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K2" target="_self">|^</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2" target="_self">|^</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="newton.html#E8:43"><i><font color="Green">E29</font></i></a>, <a class="ref" href="newton.html#T31" target="_self">Th31</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K2" target="_self">|^</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T9" target="_self">Th9</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="newton.html#T9" target="_self">Th9</a></i>
;<br/>
<b>hence </b><a NAME="E12:43"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="newton.html#K10" target="_self">In_Power</a> 0 <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="newton.html#E1:43"><i><font color="Green">E25</font></i></a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>


</div>
