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<span class="kw">let </span><font color="Maroon" title="c1">z1</font>, <font color="Maroon" title="c2">z2</font>, <font color="Maroon" title="c3">z3</font>, <font color="Maroon" title="c4">s1</font>, <font color="Maroon" title="c5">s2</font>, <font color="Maroon" title="c6">s3</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">z</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  holds   <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c1">z1</font>,<font color="Maroon" title="c2">z2</font>,<font color="Maroon" title="c3">z3</font>,<font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">s2</font>,<font color="Maroon" title="c6">s3</font>,<font color="Olive" title="b1">z</font> ) implies ( <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c2">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s2</font> &amp; <font color="Maroon" title="c3">z3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s3</font> ) )</span><br/>











<span class="kw">assume </span><a NAME="E1:32"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
for <font color="Olive" title="b1">z</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  holds   <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c1">z1</font>,<font color="Maroon" title="c2">z2</font>,<font color="Maroon" title="c3">z3</font>,<font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">s2</font>,<font color="Maroon" title="c6">s3</font>,<font color="Olive" title="b1">z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c2">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s2</font> &amp; <font color="Maroon" title="c3">z3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s3</font> )</span><br/>

<a NAME="E2:32"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A2</font></span>: 
 <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c1">z1</font>,<font color="Maroon" title="c2">z2</font>,<font color="Maroon" title="c3">z3</font>,<span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">s2</font>,<font color="Maroon" title="c6">s3</font>,<span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> </span>)</span>
 
;<br/>
<a NAME="E3:32"/>
(  <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c1">z1</font>,<font color="Maroon" title="c2">z2</font>,<font color="Maroon" title="c3">z3</font>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">s2</font>,<font color="Maroon" title="c6">s3</font>,<a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  &amp;  <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c1">z1</font>,<font color="Maroon" title="c2">z2</font>,<font color="Maroon" title="c3">z3</font>,<a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_1.html#K3" title="POLYEQ_1:func.3">Polynom</a> <font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">s2</font>,<font color="Maroon" title="c6">s3</font>,<a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E7">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:32"/>
( <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c2">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">s2</font> &amp; <font color="Maroon" title="c3">z3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">s3</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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