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<b>let </b><font color="Maroon" title="c2">seq</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">seq</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a> &amp; <font color="Maroon" title="c2">seq</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">seq</font> is <a href="valued_0.html#V10" title="VALUED_0:attr.10">non-increasing</a> implies <font color="Maroon" title="c2">seq</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a>  is <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a> )</span><br/>

<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E34">A1</font></i>: 
( <font color="Maroon" title="c2">seq</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a> &amp; <font color="Maroon" title="c2">seq</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">seq</font> is <a href="valued_0.html#V10" title="VALUED_0:attr.10">non-increasing</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">seq</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a>  is <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a></span><br/>

<a NAME="E2:43"/><b>then </b>
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> holds <br/> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">seq</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">n</font>
 
<b>by </b><i><a class="ref" href="limfunc1.html#T28" target="_self" title="LIMFUNC1:th.28">Th28</a></i>;<br/>
<b>hence </b><a NAME="E3:43"/>
<font color="Maroon" title="c2">seq</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a>  is <a href="limfunc1.html#V1" title="LIMFUNC1:attr.1">divergent_to+infty</a>
 <b>by </b><i><a class="txt" href="#E1:43"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="limfunc1.html#T62" target="_self" title="LIMFUNC1:th.62">Th62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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