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<span class="kw">let </span><font color="Maroon" title="c1">seq</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</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"> ( <font color="Maroon" title="c1">seq</font> is  <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a>  implies <font color="Maroon" title="c1">seq</font> is  <a href="comseq_3.html#V2" title="COMSEQ_3:attr.2">absolutely_summable</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:29_1_1"/>
<font color="Maroon" title="c1">seq</font> is  <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</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"> <font color="Maroon" title="c1">seq</font> is  <a href="comseq_3.html#V2" title="COMSEQ_3:attr.2">absolutely_summable</a> </span><br/>

<a NAME="E2:29_1_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">x</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon" title="c1">seq</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:29_1_1"/>
<font color="Maroon" title="c1">seq</font> is  <a href="comseq_3.html#V2" title="COMSEQ_3:attr.2">absolutely_summable</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="comseq_3.html#T51" onmouseover="rs('comseq_3/T51')" onmouseout="rh()">COMSEQ_3:51</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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