<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">b</font>, <font color="Maroon" title="c2">c</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</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>   st <font color="Maroon" title="c1">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; ( for <font color="Olive" title="b2">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_3.html#K4" title="POLYEQ_3:func.4">Polynom</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">c</font>,<font color="Olive" title="b2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) holds <br/><font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">z</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"> ( <font color="Maroon" title="c1">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; ( 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_3.html#K4" title="POLYEQ_3:func.4">Polynom</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">c</font>,<font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) implies <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">b</font></span>)</span> )</span><br/>





<a NAME="E1:9"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="polyeq_3.html#K2" title="POLYEQ_3:func.2">+</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="polyeq_3.html#K1" title="POLYEQ_3:func.1">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span>
 
;<br/>
<span class="kw">assume </span><a NAME="E2:9"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
<font color="Maroon" title="c1">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <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>  st not  <a href="polyeq_3.html#K4" title="POLYEQ_3:func.4">Polynom</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">c</font>,<font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">b</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E3:9"/><span class="lab"><font color="Green" title="E5">A3</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_3.html#K4" title="POLYEQ_3:func.4">Polynom</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">c</font>,<font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <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="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">b</font></span>)</span></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">z1</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"> <font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">b</font></span>)</span></span><br/><a NAME="E1:9_1"/>
 <a href="polyeq_3.html#K4" title="POLYEQ_3:func.4">Polynom</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c1">b</font>,<font color="Maroon" title="c2">c</font>,<font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:9"><span class="lab"><font color="Green" title="E5">A3</font></span></a></span>;<br/><a NAME="E2:9_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">b</font> <a href="polyeq_3.html#K1" title="POLYEQ_3:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">z1</font></span>)</span> <a href="polyeq_3.html#K2" title="POLYEQ_3:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">z1</font></span>)</span> <a href="polyeq_3.html#K1" title="POLYEQ_3:func.1">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T29" title="COMPLEX1:th.29">COMPLEX1:29</a></span>;<br/><a NAME="E3:9_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E6">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">z1</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="polyeq_3.html#K2" title="POLYEQ_3:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p4">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">z1</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="polyeq_3.html#K1" title="POLYEQ_3:func.1">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="polyeq_3.html#K2" title="POLYEQ_3:func.2">+</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="polyeq_3.html#K1" title="POLYEQ_3:func.1">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span>
 ;<br/><a NAME="E4:9_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">z1</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T28" title="COMPLEX1:th.28">COMPLEX1:28</a></span>;<br/><a NAME="E5:9_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">z1</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="complex1.html#T28" title="COMPLEX1:th.28">COMPLEX1:28</a></span>;<br/><a NAME="E6:9_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E7">A5</font></span>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:9"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="xcmplx_1.html#T90" title="XCMPLX_1:th.90">XCMPLX_1:90</a></span>;<br/><a NAME="E7:9_1"/>
<font color="Maroon" title="c1">b</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">z1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:9_1"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="ref" href="complex1.html#T28" title="COMPLEX1:th.28">COMPLEX1:28</a></span>;<br/><a NAME="E8:9_1"/><span class="kw">then </span>
 <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="txt" href="#E2:9"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="complex1.html#T28" title="COMPLEX1:th.28">COMPLEX1:28</a></span>;<br/><a NAME="E9:9_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">b</font></span>)</span></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="polyeq_3.html#K1" title="POLYEQ_3:func.1">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:9_1"><span class="lab"><font color="Green" title="E7">A5</font></span></a>, <a class="ref" href="complex1.html#T29" title="COMPLEX1:th.29">COMPLEX1:29</a></span>;<br/><span class="kw">hence </span><a NAME="E10:9_1"/>
<font color="Maroon" title="c4">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">b</font></span>)</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:9"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K10" title="COMPLEX1:func.10">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="complex1.html#K13" title="COMPLEX1:func.13">/</a> <font color="Maroon" title="c1">b</font></span>)</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/>


</div>
