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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">z</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;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</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="c3">z</font> implies <font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">z</font> )</span><br/>

<b>assume </b><a NAME="E1:40"/><i><font color="Green" title="E30">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;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">y</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="c3">z</font> )
 ; <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="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">z</font></span><br/>

<a NAME="E2:40"/><i><font color="Green" title="E31">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <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>
 
<b>by </b><i><a class="ref" href="complsp2.html#T5" target="_self" title="COMPLSP2:th.5">Th5</a></i>;<br/>
<font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">z</font></span>)</span> = 
<font color="Maroon" title="c1">x</font> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complsp1.html#K5" title="COMPLSP1:func.5">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">z</font></span>)</span>
<b>by </b><i><a class="txt" href="complsp2.html#E1:40"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="complsp2.html#T39" target="_self" title="COMPLSP2:th.39">Th39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">z</font>
<b>by </b><i><a class="txt" href="complsp2.html#E1:40"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="complsp2.html#E2:40"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="complsp2.html#T28" target="_self" title="COMPLSP2:th.28">Th28</a></i>
;<br/>
<b>hence </b><a NAME="E4:40"/>
<font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <font color="Maroon" title="c3">z</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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