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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( 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> ) implies ( <font color="Maroon" title="c1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c4">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font> &amp; <font color="Maroon" title="c5">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b5</font> ) )</span><br/>

<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E8">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c4">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font> &amp; <font color="Maroon" title="c5">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b5</font> )</span><br/>

<a NAME="E2:12"/><b>then </b><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c1">a1</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">a3</font>
 
<b>by </b><i><a class="ref" href="polyeq_2.html#T8" target="_self" title="POLYEQ_2:th.8">Th8</a></i>;<br/>
<a NAME="E3:12"/><i><font color="Green" title="E10">A3</font></i>: 
<font color="Maroon" title="c2">a2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c4">a4</font>
 
<b>by </b><i><a class="txt" href="polyeq_2.html#E1:12"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="polyeq_2.html#T8" target="_self" title="POLYEQ_2:th.8">Th8</a></i>;<br/>
<a NAME="E4:12"/><i><font color="Green" title="E11">A4</font></i>: 
<font color="Maroon" title="c5">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b5</font>
 
<b>by </b><i><a class="txt" href="polyeq_2.html#E1:12"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="polyeq_2.html#T7" target="_self" title="POLYEQ_2:th.7">Th7</a></i>;<br/>
<a NAME="E5:12"/><i><font color="Green" title="E12">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>,2 <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>,2
 
<b>by </b><i><a class="txt" href="polyeq_2.html#E1:12"><i><font color="Green" title="E8">A1</font></i></a></i>;<br/>
<a NAME="E6:12"/><i><font color="Green" title="E13">A6</font></i>: 
2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 16
 
<b>by </b><i><a class="ref" href="asympt_1.html#T46" title="ASYMPT_1:th.46">ASYMPT_1:46</a></i>;<br/>
<a NAME="E7:12"/><i><font color="Green" title="E14">A7</font></i>: 
2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8
 
<b>by </b><i><a class="ref" href="asympt_1.html#T45" title="ASYMPT_1:th.45">ASYMPT_1:45</a></i>;<br/>
<a NAME="E8:12"/><i><font color="Green" title="E15">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> 2</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> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="polyeq_2.html#E1:12"><i><font color="Green" title="E8">A1</font></i></a></i>;<br/>
<a NAME="E9:12"/><i><font color="Green" title="E16">A9</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 2</span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 16
 
<b>by </b><i><a class="txt" href="polyeq_2.html#E6:12"><i><font color="Green" title="E13">A6</font></i></a>, <a class="txt" href="polyeq_2.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a>, <a class="ref" href="power.html#T1" title="POWER:th.1">POWER:1</a></i>;<br/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 2</span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 2</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> 2</span>)</span>
<b>by </b><i><a class="ref" href="polyeq_2.html#T4" target="_self" title="POLYEQ_2:th.4">Th4</a></i>
<br/>.= 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 2</span>)</span>

;<br/>
<b>hence </b><a NAME="E11:12"/>
( <font color="Maroon" title="c1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c4">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font> &amp; <font color="Maroon" title="c5">a5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b5</font> )
 <b>by </b><i><a class="txt" href="polyeq_2.html#E2:12"><i><font color="Green" title="E9">A2</font></i></a>, <a class="txt" href="polyeq_2.html#E3:12"><i><font color="Green" title="E10">A3</font></i></a>, <a class="txt" href="polyeq_2.html#E4:12"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="polyeq_2.html#E5:12"><i><font color="Green" title="E12">A5</font></i></a>, <a class="txt" href="polyeq_2.html#E6:12"><i><font color="Green" title="E13">A6</font></i></a>, <a class="txt" href="polyeq_2.html#E7:12"><i><font color="Green" title="E14">A7</font></i></a>, <a class="txt" href="polyeq_2.html#E8:12"><i><font color="Green" title="E15">A8</font></i></a>, <a class="txt" href="polyeq_2.html#E9:12"><i><font color="Green" title="E16">A9</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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