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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>( <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="taylor_1.html#K5" target="_self">diff</a> <font color="Maroon">f</font>,<font color="Maroon">Z</font></span>)</span> <a href="seqfunc.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="newton.html#K2">|^</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="newton.html#K6">!</a> </span>)</span>;<br/>
<b>let </b><font color="Maroon">s1</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>, <font color="Maroon">s2</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:35_1_2"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">n</font> being <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds  <font color="Maroon">s1</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">n</font>)
 <b>and </b><br/><a NAME="E2:35_1_2"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">n</font> being <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds  <font color="Maroon">s2</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">n</font>)
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:35_1_2_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 ;<br/><b>reconsider </b><font color="Maroon">n</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="taylor_1.html#D1" target="_self">Def1</a></i>;<br/><b>thus </b><font color="Maroon">s1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">n</font>)
<b>by </b><i/>
<br/>.= 
<font color="Maroon">s2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:35_1_2"/>
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font>
 <b>by </b><i><a class="ref" href="seq_1.html#T8">SEQ_1:8</a></i>;<br/>


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