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<span class="kw">let </span><font color="Maroon" title="c1">x1</font>, <font color="Maroon" title="c2">x2</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="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x1</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">x2</font> implies <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><span class="p2">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <font color="Maroon" title="c2">x2</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:66"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">x1</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">x2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><span class="p2">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <font color="Maroon" title="c2">x2</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span></span><br/>

<a NAME="E2:66"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <font color="Maroon" title="c2">x2</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">x1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#T5" target="_self" title="COMPLSP2:th.5">Th5</a></span>;<br/>
<span class="kw">then </span><span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><span class="p2">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <font color="Maroon" title="c2">x2</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> = 
 <a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x1</font>,<span class="p2">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <font color="Maroon" title="c2">x2</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="complsp2.html#T67" target="_self" title="COMPLSP2:th.67">Th67</a></span>
<br/>.= 
 <a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <span class="p1">(<span class="default"><a href="binop_2.html#K1" title="BINOP_2:func.1">-</a> <span class="p2"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:66"><span class="lab"><font color="Green" title="E50">A1</font></span></a>, <a class="ref" href="complsp2.html#T68" target="_self" title="COMPLSP2:th.68">Th68</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:66"/>
<span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><span class="p2">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p2">(<span class="default"><a href="seq_4.html#K11" title="SEQ_4:func.11">-</a> <font color="Maroon" title="c2">x2</font></span>)</span></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="complsp2.html#K8" title="COMPLSP2:func.8">|(</a><span class="default"><font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span><a href="complsp2.html#K8" title="COMPLSP2:func.8">)|</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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