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<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="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font> )</span><br/>





<b>reconsider </b><font color="Maroon" title="c4">z3'</font> = <font color="Maroon" title="c3">z3</font>, <font color="Maroon" title="c5">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="E2:45"/><i><font color="Green" title="E10">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="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font> )</span><br/>

<b>assume </b><a NAME="E3:45"/><i><font color="Green" title="E11">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="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:45_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="#E3:45"><i><font color="Green" title="E11">A2</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="45_1_1"><b>suppose </b></a><a NAME="E1:45_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="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font></span><br/><div class="add"><b>hence </b><font color="Maroon" title="c2">z1</font> = 
<font color="Maroon" title="c4">z3'</font> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <font color="Maroon" title="c5">z2'</font>
<b>by </b><i><a class="txt" href="#E2:45"><i><font color="Green" title="E10">A1</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#T90" title="XCMPLX_1:th.90">XCMPLX_1:90</a></i>
<br/>.= 
<font color="Maroon" title="c3">z3</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font>
<b>by </b><i><a class="txt" href="#E2:45"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="complfld.html#T8" target="_self" title="COMPLFLD:th.8">Th8</a></i>
;<br/> <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="45_1_2"><b>suppose </b></a><a NAME="E1:45_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="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font></span><br/><div class="add"><b>hence </b><font color="Maroon" title="c2">z1</font> = 
<font color="Maroon" title="c4">z3'</font> <a href="binop_2.html#K6" title="BINOP_2:func.6">/</a> <font color="Maroon" title="c5">z2'</font>
<b>by </b><i><a class="txt" href="#E2:45"><i><font color="Green" title="E10">A1</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#T90" title="XCMPLX_1:th.90">XCMPLX_1:90</a></i>
<br/>.= 
<font color="Maroon" title="c3">z3</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <font color="Maroon" title="c1">z2</font>
<b>by </b><i><a class="txt" href="#E2:45"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="complfld.html#T8" target="_self" title="COMPLFLD:th.8">Th8</a></i>
;<br/> <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>

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