<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">seq</font> is  <a href="valued_0.html#NV13" title="VALUED_0:NV.13">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/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:70"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
<font color="Maroon" title="c2">seq</font> is  <a href="valued_0.html#NV13" title="VALUED_0:NV.13">non-zero</a> 
 <span class="kw">and </span><br/><a NAME="E2:70"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
( <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>  )
 <span class="kw">and </span><br/><a NAME="E3:70"/><span class="lab"><font color="Green" title="E35">A3</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E4:70"/>
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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:70"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="txt" href="#E2:70"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="txt" href="#E3:70"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="ref" href="limfunc1.html#T28" target="_self" title="LIMFUNC1:th.28">Th28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:70"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:70"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="limfunc1.html#T62" target="_self" title="LIMFUNC1:th.62">Th62</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
