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<b>let </b><font color="Maroon">s</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<a NAME="E1:45"/>
<font color="Maroon">s</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">m1</font> = <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">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">l1</font> = <font color="Maroon">s</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">m1</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/>
<a NAME="E4:45"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="newton.html#K10" target="_self">In_Power</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E5:45"/><b>then </b>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="newton.html#K10" target="_self">In_Power</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E6:45"/><b>then </b>
<font color="Maroon">s</font> <a href="xcmplx_0.html#K2">+</a> 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">a</font>,<font color="Maroon">b</font> <a href="newton.html#K10" target="_self">In_Power</a> <font color="Maroon">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T6">FINSEQ_1:6</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="newton.html#K10" target="_self">In_Power</a> <font color="Maroon">s</font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="newton.html#K9" target="_self">choose</a> <font color="Maroon">s</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="newton.html#K2" target="_self">|^</a> <font color="Maroon">l1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="newton.html#K2" target="_self">|^</a> <font color="Maroon">m1</font></span>)</span>
<b>by </b><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">a</font> <a href="newton.html#K2" target="_self">|^</a> <font color="Maroon">l1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="newton.html#K2" target="_self">|^</a> <font color="Maroon">m1</font></span>)</span>
<b>by </b><i/>
<br/>.= 
1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="newton.html#K2" target="_self">|^</a> <font color="Maroon">m1</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">b</font> <a href="newton.html#K2" target="_self">|^</a> <font color="Maroon">s</font>

;<br/>
<b>hence </b><a NAME="E8:45"/>
<span class="p1">(<span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="newton.html#K10" target="_self">In_Power</a> <font color="Maroon">s</font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="newton.html#K2" target="_self">|^</a> <font color="Maroon">s</font>
 ;<br/>


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