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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">d</font>, <font color="Maroon" title="c5">a'</font>, <font color="Maroon" title="c6">b'</font>, <font color="Maroon" title="c7">c'</font>, <font color="Maroon" title="c8">d'</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</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">z</font> being <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds   <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>,<font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font>,<font color="Maroon" title="c8">d'</font>,<font color="Olive" title="b1">z</font> ) implies ( <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a'</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b'</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c'</font> &amp; <font color="Maroon" title="c4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d'</font> ) )</span><br/>















<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E6">A1</font></i>: 
for <font color="Olive" title="b1">z</font> being <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds   <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>,<font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font>,<font color="Maroon" title="c8">d'</font>,<font color="Olive" title="b1">z</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">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a'</font> &amp; <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b'</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c'</font> &amp; <font color="Maroon" title="c4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d'</font> )</span><br/>

<a NAME="E2:12"/><b>then </b><i><font color="Green" title="E7">A2</font></i>: 
 <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</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_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font>,<font color="Maroon" title="c8">d'</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<a NAME="E3:12"/><i><font color="Green" title="E8">A3</font></i>: 
 <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font>,<font color="Maroon" title="c8">d'</font>,1
 
<b>by </b><i><a class="txt" href="polyeq_3.html#E1:12"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/>
<a NAME="E4:12"/><i><font color="Green" title="E9">A4</font></i>: 
 <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font>,<font color="Maroon" title="c8">d'</font>,<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="polyeq_3.html#E1:12"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/>
<a NAME="E5:12"/><i><font color="Green" title="E10">A5</font></i>: 
 <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_1.html#K7" title="POLYEQ_1:func.7">Polynom</a> <font color="Maroon" title="c5">a'</font>,<font color="Maroon" title="c6">b'</font>,<font color="Maroon" title="c7">c'</font>,<font color="Maroon" title="c8">d'</font>,2
 
<b>by </b><i><a class="txt" href="polyeq_3.html#E1:12"><i><font color="Green" title="E6">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:12"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a'</font>
 <b>by </b><i><a class="txt" href="polyeq_3.html#E2:12"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="polyeq_3.html#E3:12"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="polyeq_3.html#E4:12"><i><font color="Green" title="E9">A4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b'</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c'</font> &amp; <font color="Maroon" title="c4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d'</font> )</span><br/>

<b>thus </b><a NAME="E7:12"/>
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b'</font>
 <b>by </b><i><a class="txt" href="polyeq_3.html#E2:12"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="polyeq_3.html#E3:12"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="polyeq_3.html#E4:12"><i><font color="Green" title="E9">A4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c'</font> &amp; <font color="Maroon" title="c4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d'</font> )</span><br/>

<b>thus </b><a NAME="E8:12"/>
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">c'</font>
 <b>by </b><i><a class="txt" href="polyeq_3.html#E2:12"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="polyeq_3.html#E3:12"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="polyeq_3.html#E4:12"><i><font color="Green" title="E9">A4</font></i></a>, <a class="txt" href="polyeq_3.html#E5:12"><i><font color="Green" title="E10">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d'</font></span><br/>

<b>thus </b><a NAME="E9:12"/>
<font color="Maroon" title="c4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">d'</font>
 <b>by </b><i><a class="txt" href="polyeq_3.html#E2:12"><i><font color="Green" title="E7">A2</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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