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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">x</font> <a href="valued_1.html#K1" title="VALUED_1:func.1">+</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font></span><br/>

<a NAME="E1:34"/><span class="lab"><font color="Green" title="E24">A</font></span>: 
<font color="Maroon" title="c1">x</font> is    <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> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="complsp2.html#E8"><span class="lab"><font color="Green" title="E5">Lm4</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">x9</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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></span>;<br/>
<font color="Maroon" title="c1">x</font> <a href="valued_1.html#K1" title="VALUED_1:func.1">+</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> = 
<font color="Maroon" title="c1">x</font> <a href="valued_1.html#K1" title="VALUED_1:func.1">+</a> <span class="p1">(<span class="default"><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> <a href="complsp2.html#K9" title="COMPLSP2:func.9">|-&gt;</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#D15" title="SEQ_4:def.15">SEQ_4:def 15</a></span>
<br/>.= 
<a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a>  <a href="funcop_1.html#K3" title="FUNCOP_1:func.3">.:</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><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> <a href="complsp2.html#K9" title="COMPLSP2:func.9">|-&gt;</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#D9" title="SEQ_4:def.9">SEQ_4:def 9</a>, <a class="txt" href="#E1:34"><span class="lab"><font color="Green" title="E24">A</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c2">x9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#T1" title="BINOP_2:th.1">BINOP_2:1</a>, <a class="ref" href="finseqop.html#T57" title="FINSEQOP:th.57">FINSEQOP:57</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:34"/>
<font color="Maroon" title="c1">x</font> <a href="valued_1.html#K1" title="VALUED_1:func.1">+</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font>
 ; <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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