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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 implies <a href="irrat_1.html#K4" title="IRRAT_1:func.4">dseq</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <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> <a href="irrat_1.html#K5" title="IRRAT_1:func.5">eseq</a> )</span><br/>

<span class="kw">assume </span><a NAME="E1:35"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 ; <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"> <a href="irrat_1.html#K4" title="IRRAT_1:func.4">dseq</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <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> <a href="irrat_1.html#K5" title="IRRAT_1:func.5">eseq</a></span><br/>

<a NAME="E2:35"/><span class="kw">then </span>
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> (  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="irrat_1.html#K3" title="IRRAT_1:func.3">cseq</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> &amp; <span class="p1">(<span class="default"><a href="irrat_1.html#K3" title="IRRAT_1:func.3">cseq</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <a href="irrat_1.html#K5" title="IRRAT_1:func.5">eseq</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="irrat_1.html#T14" target="_self" onmouseover="rs('irrat_1/T14')" onmouseout="rh()">Th14</a></span>;<br/>
<a NAME="E3:35"/><span class="kw">then </span>
 <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="irrat_1.html#K3" title="IRRAT_1:func.3">cseq</a> <font color="Maroon" title="c1">n</font></span>)</span> <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> <a href="irrat_1.html#K5" title="IRRAT_1:func.5">eseq</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="irrat_1.html#T23" target="_self" onmouseover="rs('irrat_1/T23')" onmouseout="rh()">Th23</a>, <a class="ref" href="series_1.html#T20" onmouseover="rs('series_1/T20')" onmouseout="rh()">SERIES_1:20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:35"/>
<a href="irrat_1.html#K4" title="IRRAT_1:func.4">dseq</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">n</font> <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> <a href="irrat_1.html#K5" title="IRRAT_1:func.5">eseq</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="irrat_1.html#T21" target="_self" onmouseover="rs('irrat_1/T21')" onmouseout="rh()">Th21</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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