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

<b>let </b><font color="Maroon" title="c1">z2</font>, <font color="Maroon" title="c2">z1</font>, <font color="Maroon" title="c3">z3</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">z2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  &amp; ( <font color="Maroon" title="c2">z1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> or <font color="Maroon" title="c1">z2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> ) implies ( <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> &amp; <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">z3</font> ) )</span><br/>





<b>reconsider </b><font color="Maroon" title="c4">z2'</font> = <font color="Maroon" title="c1">z2</font> as    <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>  <b>by </b><i><a class="ref" href="complfld.html#D1" target="_self" title="COMPLFLD:def.1">Def1</a></i>;<br/>
<b>assume </b><a NAME="E2:18"/><i><font color="Green" title="E9">A1</font></i>: 
<font color="Maroon" title="c1">z2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c2">z1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> &amp; not <font color="Maroon" title="c1">z2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> ) or ( <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> &amp; <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">z3</font> ) )</span><br/>

<b>assume </b><a NAME="E3:18"/><i><font color="Green" title="E10">A2</font></i>: 
( <font color="Maroon" title="c2">z1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> or <font color="Maroon" title="c1">z2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> &amp; <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">z3</font> )</span><br/>

<a NAME="E4:18"/><i><font color="Green" title="E11">A3</font></i>: 
<font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">z2'</font> <a href="binop_2.html#K2" title="BINOP_2:func.2">"</a> 
 
<b>by </b><i><a class="txt" href="#E2:18"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="complfld.html#T7" target="_self" title="COMPLFLD:th.7">Th7</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:18_1"/>
( <font color="Maroon" title="c2">z1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> or <font color="Maroon" title="c1">z2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> )
 </span><b>by </b><i><a class="txt" href="#E3:18"><i><font color="Green" title="E10">A2</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1"><b>suppose </b></a><a NAME="E1:18_1_1"/>
<font color="Maroon" title="c2">z1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c1">z2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> &amp; <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">z3</font> )</span><br/><div class="add"><b>hence </b><a NAME="E2:18_1_1"/>
( <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> &amp; <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">z3</font> )
 <b>by </b><i><a class="txt" href="#E2:18"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E4:18"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="complfld.html#T9" target="_self" title="COMPLFLD:th.9">Th9</a>, <a class="ref" href="xcmplx_1.html#T204" title="XCMPLX_1:th.204">XCMPLX_1:204</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_2"><b>suppose </b></a><a NAME="E1:18_1_2"/>
<font color="Maroon" title="c1">z2</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> &amp; <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">z3</font> )</span><br/><div class="add"><b>hence </b><a NAME="E2:18_1_2"/>
( <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z3</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> &amp; <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">z2</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">z3</font> )
 <b>by </b><i><a class="txt" href="#E2:18"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E4:18"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="complfld.html#T9" target="_self" title="COMPLFLD:th.9">Th9</a>, <a class="ref" href="xcmplx_1.html#T204" title="XCMPLX_1:th.204">XCMPLX_1:204</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
