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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:36"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 ;<br/>

<a NAME="E2:36"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E3:36"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
;<br/>
<a NAME="E4:36"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <br/>( 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="irrat_1.html#K3" target="_self">cseq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="irrat_1.html#K3" target="_self">cseq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <a href="irrat_1.html#K5" target="_self">eseq</a>  <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="irrat_1.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E5:36"/><b>then </b>
 <a href="series_1.html#K2">Sum</a> <span class="p1">(<span class="default"><a href="irrat_1.html#K3" target="_self">cseq</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="series_1.html#K2">Sum</a> <a href="irrat_1.html#K5" target="_self">eseq</a> 
 
<b>by </b><i><a class="ref" href="irrat_1.html#T24" target="_self">Th24</a>, <a class="ref" href="series_1.html#T24">SERIES_1:24</a></i>;<br/>
<b>hence </b><a NAME="E6:36"/>
<a href="irrat_1.html#K4" target="_self">dseq</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="series_1.html#K2">Sum</a> <a href="irrat_1.html#K5" target="_self">eseq</a> 
 <b>by </b><i><a class="txt" href="irrat_1.html#E3:36"><i><font color="Green">E34</font></i></a>, <a class="ref" href="irrat_1.html#T22" target="_self">Th22</a></i>;<br/>


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