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<span class="kw">let </span><font color="Maroon" title="c1">x</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">c</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"><a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <font color="Olive" title="b1">c</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">c</font> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">c</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span><br/>



<a NAME="E1:53"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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="c2">c</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</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="c1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#T3" target="_self" title="COMPLSP2:th.3">Th3</a></span>;<br/>
<a NAME="E2:53"/><span class="lab"><font color="Green" title="E41">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</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="c1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#T3" target="_self" title="COMPLSP2:th.3">Th3</a></span>;<br/>
<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="c2">c</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="seq_4.html#K9" title="SEQ_4:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> 1</span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="seq_4.html#K9" title="SEQ_4:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span> <a href="seq_4.html#K9" title="SEQ_4:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#T53" target="_self" title="COMPLSP2:th.53">Th53</a></span>
<br/>.= 
 <a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="seq_4.html#K10" title="SEQ_4:func.10">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:53"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="complsp2.html#T39" target="_self" title="COMPLSP2:th.39">Th39</a></span>
<br/>.= 
 <a href="seq_4.html#K18" title="SEQ_4:func.18">-</a> <span class="p1">(<span class="default"><a href="seq_4.html#K17" title="SEQ_4:func.17">0c</a> <span class="p2">(<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></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:53"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="complsp2.html#T34" target="_self" title="COMPLSP2:th.34">Th34</a></span>
<br/>.= 
 <a href="seq_4.html#K17" title="SEQ_4:func.17">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="complsp2.html#E60"><span class="lab"><font color="Green" title="E38">Lm2</font></span></a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:53"/>
<span class="p1">(<span class="default"><a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="seq_4.html#K12" title="SEQ_4:func.12">*</a> <font color="Maroon" title="c1">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="txt" href="#E2:53"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="complsp2.html#T32" target="_self" title="COMPLSP2:th.32">Th32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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