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<a NAME="E1:52_1_1"/>
<font color="Maroon" title="c2">h</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">n</font> is <a href="ndiff_1.html#V2" title="NDIFF_1:attr.2">convergent_to_0</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:52_1_1_1"/><i><font color="Green" title="E39">A1</font></i>: 
( <font color="Maroon" title="c2">h</font> <a href="ndiff_1.html#NR1" title="NDIFF_1:NR.1">is_not_0</a>  &amp; <font color="Maroon" title="c2">h</font> is <a href="normsp_1.html#V4" title="NORMSP_1:attr.4">convergent</a> &amp;  <a href="normsp_1.html#K8" title="NORMSP_1:func.8">lim</a> <font color="Maroon" title="c2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">S</font> )
 
<b>by </b><i><a class="ref" href="ndiff_1.html#D4" target="_self" title="NDIFF_1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E2:52_1_1_1"/>
<font color="Maroon" title="c2">h</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">n</font> <a href="ndiff_1.html#NR1" title="NDIFF_1:NR.1">is_not_0</a> 
 <b>by </b><i><a class="ref" href="ndiff_1.html#T17" target="_self" title="NDIFF_1:th.17">Th17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ndiff_1.html#D4" target="_self" title="NDIFF_1:def.4">NDIFF_1:def 4</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">h</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">n</font> is <a href="normsp_1.html#V4" title="NORMSP_1:attr.4">convergent</a> &amp;  <a href="normsp_1.html#K8" title="NORMSP_1:func.8">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">h</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">S</font> )</span><br/>

<b>thus </b><a NAME="E3:52_1_1_1"/>
( <font color="Maroon" title="c2">h</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">n</font> is <a href="normsp_1.html#V4" title="NORMSP_1:attr.4">convergent</a> &amp;  <a href="normsp_1.html#K8" title="NORMSP_1:func.8">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">h</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">S</font> )
 <b>by </b><i><a class="txt" href="ndiff_1.html#E1:52_1_1_1"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="lopban_3.html#T14" title="LOPBAN_3:th.14">LOPBAN_3:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:52_1_1"/>
<font color="Maroon" title="c2">h</font> <a href="lopban_3.html#K2" title="LOPBAN_3:func.2">^\</a> <font color="Maroon" title="c3">n</font> is <a href="ndiff_1.html#V2" title="NDIFF_1:attr.2">convergent_to_0</a>
 ; <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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