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<span class="kw">let </span><font color="Maroon" title="c2">z</font> be   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Maroon" title="c2">z</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="sin_cos.html#K4" title="SIN_COS:func.4">rExpSeq</a></span>)</span></span><br/>

<span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="comseq_3.html#K10" title="COMSEQ_3:func.10">Partial_Sums</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="sin_cos.html#K3" title="SIN_COS:func.3">ExpSeq</a></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> = 
<span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="sin_cos.html#K3" title="SIN_COS:func.3">ExpSeq</a></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="series_1.html#D1" onmouseover="rs('series_1/D1')" onmouseout="rh()">SERIES_1:def 1</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T3" target="_self" onmouseover="rs('sin_cos/T3')" onmouseout="rh()">Th3</a>, <a class="ref" href="complex1.html#T48" onmouseover="rs('complex1/T48')" onmouseout="rh()">COMPLEX1:48</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:34"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><font color="Maroon" title="c2">z</font></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="sin_cos.html#K4" title="SIN_COS:func.4">rExpSeq</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T16" target="_self" onmouseover="rs('sin_cos/T16')" onmouseout="rh()">Th16</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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