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<span class="kw">let </span><font color="Maroon" title="c1">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">R1</font>, <font color="Olive" title="b2">R2</font> being  <font color="Maroon" title="c1">i</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <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>  holds   <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">R1</font> <a href="rvsum_2.html#K4" title="RVSUM_2:func.4">+</a> <font color="Olive" title="b2">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Olive" title="b1">R1</font></span>)</span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Olive" title="b2">R2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">R1</font>, <font color="Maroon" title="c3">R2</font> be  <font color="Maroon" title="c1">i</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>   <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="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R1</font> <a href="rvsum_2.html#K4" title="RVSUM_2:func.4">+</a> <font color="Maroon" title="c3">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c2">R1</font></span>)</span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c3">R2</font></span>)</span></span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">T1</font> = <font color="Maroon" title="c2">R1</font>, <font color="Maroon" title="c5">T2</font> = <font color="Maroon" title="c3">R2</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">i</font> <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#T131" title="FINSEQ_2:th.131">FINSEQ_2:131</a></span>;<br/>
<span class="kw">thus </span> <a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R1</font> <a href="rvsum_2.html#K4" title="RVSUM_2:func.4">+</a> <font color="Maroon" title="c3">R2</font></span>)</span> = 
<a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <font color="Maroon" title="c4">T1</font></span>)</span>,<span class="p1">(<span class="default"><a href="binop_2.html#K27" title="BINOP_2:func.27">addcomplex</a> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <font color="Maroon" title="c5">T2</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="setwop_2.html#T35" title="SETWOP_2:th.35">SETWOP_2:35</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c2">R1</font></span>)</span> <a href="binop_2.html#K3" title="BINOP_2:func.3">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K17" title="RVSUM_1:func.17">Sum</a> <font color="Maroon" title="c3">R2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#D3" title="BINOP_2:def.3">BINOP_2:def 3</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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