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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font></span>)</span> implies ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c1">x</font> ) )</span><br/>

<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E23">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c1">x</font> )</span><br/>

<b>reconsider </b><font color="Maroon" title="c3">y'</font> = <font color="Maroon" title="c2">y</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">x'</font> = <font color="Maroon" title="c1">x</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></i>;<br/>
<a NAME="E4:33"/><i><font color="Green" title="E24">A2</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="finseqop.html#K1" title="FINSEQOP:func.1">.:</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>
 
<b>by </b><i><a class="ref" href="complsp1.html#D7" title="COMPLSP1:def.7">COMPLSP1:def 7</a></i>;<br/>
<a NAME="E5:33"/><i><font color="Green" title="E25">A3</font></i>: 
 <a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K25" title="BINOP_2:func.25">compcomplex</a>  <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c2">y</font>
 
<b>by </b><i><a class="ref" href="complsp1.html#D9" title="COMPLSP1:def.9">COMPLSP1:def 9</a></i>;<br/>
<a NAME="E6:33"/>
<font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="complsp2.html#K9" title="COMPLSP2:func.9">|-&gt;</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> 
 
<b>by </b><i><a class="txt" href="complsp2.html#E1:33"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="complsp1.html#D13" title="COMPLSP1:def.13">COMPLSP1:def 13</a></i>;<br/>
<a NAME="E7:33"/><b>then </b>
<font color="Maroon" title="c4">x'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp2.html#K5" title="COMPLSP2:func.5">-</a> <font color="Maroon" title="c3">y'</font>
 
<b>by </b><i><a class="txt" href="complsp2.html#E1:33"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="complsp2.html#E4:33"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="complsp2.html#E5:33"><i><font color="Green" title="E25">A3</font></i></a>, <a class="ref" href="binop_2.html#T1" title="BINOP_2:th.1">BINOP_2:1</a>, <a class="ref" href="complsp1.html#T7" title="COMPLSP1:th.7">COMPLSP1:7</a>, <a class="ref" href="complsp1.html#T8" title="COMPLSP1:th.8">COMPLSP1:8</a>, <a class="ref" href="finseqop.html#T78" title="FINSEQOP:th.78">FINSEQOP:78</a></i>;<br/>
<b>hence </b><a NAME="E8:33"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c1">x</font> )
 ; <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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