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<b>let </b><font color="Maroon" title="c1">a1</font>, <font color="Maroon" title="c2">a2</font>, <font color="Maroon" title="c3">a3</font>, <font color="Maroon" title="c4">a4</font>, <font color="Maroon" title="c5">a5</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c9">b4</font>, <font color="Maroon" title="c10">b5</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>assume </b><a NAME="E1:10"/><i><font color="Green" title="E6">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds   <a href="polyeq_2.html#K1" title="POLYEQ_2:func.1">Polynom</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">a2</font>,<font color="Maroon" title="c3">a3</font>,<font color="Maroon" title="c4">a4</font>,<font color="Maroon" title="c5">a5</font>,<font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_2.html#K1" title="POLYEQ_2:func.1">Polynom</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>,<font color="Maroon" title="c10">b5</font>,<font color="Olive" title="b1">x</font>
 ;<br/>

<a NAME="E2:10"/><b>then </b><i><font color="Green" title="E7">A2</font></i>: 
 <a href="polyeq_2.html#K1" title="POLYEQ_2:func.1">Polynom</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">a2</font>,<font color="Maroon" title="c3">a3</font>,<font color="Maroon" title="c4">a4</font>,<font color="Maroon" title="c5">a5</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_2.html#K1" title="POLYEQ_2:func.1">Polynom</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>,<font color="Maroon" title="c10">b5</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<a NAME="E3:10"/><i><font color="Green" title="E8">A3</font></i>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="newton.html#T16" title="NEWTON:th.16">NEWTON:16</a></i>;<br/>
<a NAME="E4:10"/><i><font color="Green" title="E9">A4</font></i>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="newton.html#T16" title="NEWTON:th.16">NEWTON:16</a></i>;<br/>
<a NAME="E5:10"/><i><font color="Green" title="E10">A5</font></i>: 
 <a href="polyeq_2.html#K1" title="POLYEQ_2:func.1">Polynom</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">a2</font>,<font color="Maroon" title="c3">a3</font>,<font color="Maroon" title="c4">a4</font>,<font color="Maroon" title="c5">a5</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_2.html#K1" title="POLYEQ_2:func.1">Polynom</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>,<font color="Maroon" title="c10">b5</font>,1
 
<b>by </b><i><a class="txt" href="polyeq_2.html#E1:10"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/>
<a NAME="E6:10"/><i><font color="Green" title="E11">A6</font></i>: 
1 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="newton.html#T15" title="NEWTON:th.15">NEWTON:15</a></i>;<br/>
<a NAME="E7:10"/><i><font color="Green" title="E12">A7</font></i>: 
1 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="newton.html#T15" title="NEWTON:th.15">NEWTON:15</a></i>;<br/>
<b>set </b><font color="Maroon" title="c11">m</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">a2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">a3</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">a4</font>;<br/>
<b>set </b><font color="Maroon" title="c12">n</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">b1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">b2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">b3</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c9">b4</font>;<br/>
<b>set </b><font color="Maroon" title="c13">x</font> =  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1;<br/>
<a NAME="E8:10"/><i><font color="Green" title="E13">A8</font></i>: 
 <a href="polyeq_2.html#K1" title="POLYEQ_2:func.1">Polynom</a> <font color="Maroon" title="c1">a1</font>,<font color="Maroon" title="c2">a2</font>,<font color="Maroon" title="c3">a3</font>,<font color="Maroon" title="c4">a4</font>,<font color="Maroon" title="c5">a5</font>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_2.html#K1" title="POLYEQ_2:func.1">Polynom</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>,<font color="Maroon" title="c10">b5</font>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="polyeq_2.html#E1:10"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/>
<a NAME="E9:10"/>
( <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 4 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 4 )
 
<b>by </b><i><a class="ref" href="polyeq_2.html#T4" target="_self" title="POLYEQ_2:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E10:10"/>
( <font color="Maroon" title="c5">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b5</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c2">a2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">a3</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c4">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">b1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c7">b2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">b3</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">b4</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">a2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">a3</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">b1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">b2</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c8">b3</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c9">b4</font> )
 <b>by </b><i><a class="txt" href="polyeq_2.html#E2:10"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="polyeq_2.html#E3:10"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="polyeq_2.html#E4:10"><i><font color="Green" title="E9">A4</font></i></a>, <a class="txt" href="polyeq_2.html#E5:10"><i><font color="Green" title="E10">A5</font></i></a>, <a class="txt" href="polyeq_2.html#E6:10"><i><font color="Green" title="E11">A6</font></i></a>, <a class="txt" href="polyeq_2.html#E7:10"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="polyeq_2.html#E8:10"><i><font color="Green" title="E13">A8</font></i></a></i>;<br/>


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