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<b>let </b><font color="Maroon" title="c1">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"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be  <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font></span>)</span></span><br/>



<b>reconsider </b><font color="Maroon" title="c4">aa</font> = <font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c5">bb</font> = <font color="Maroon" title="c3">b</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="xcmplx_0.html#D2" title="XCMPLX_0:def.2">XCMPLX_0:def 2</a></i>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">aa</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="complsp1.html#K3" title="COMPLSP1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <font color="Maroon" title="c5">bb</font></span>)</span> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T63" target="_self" title="COMPLSP2:th.63">Th63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font></span>)</span>
<b>by </b><i><a class="ref" href="complsp2.html#T54" target="_self" title="COMPLSP2:th.54">Th54</a></i>
;<br/>
<b>hence </b><a NAME="E3:61"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="complsp1.html#K4" title="COMPLSP1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="complsp1.html#K6" title="COMPLSP1:func.6">*</a> <font color="Maroon" title="c1">z</font></span>)</span>
 ; <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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