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<a NAME="E1:47_1_1"/>
<font color="Maroon" title="c3">h</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Maroon" title="c4">n</font> is <a href="cfdiff_1.html#V1" title="CFDIFF_1:attr.1">convergent_to_0</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:47_1_1_1"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c3">h</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a> &amp; <font color="Maroon" title="c3">h</font> is <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">convergent</a> &amp;  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="cfdiff_1.html#D1" target="_self" title="CFDIFF_1:def.1">Def1</a></i>;<br/>
<b>thus </b><a NAME="E2:47_1_1_1"/>
<font color="Maroon" title="c3">h</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Maroon" title="c4">n</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cfdiff_1.html#D1" target="_self" title="CFDIFF_1:def.1">CFDIFF_1:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">h</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Maroon" title="c4">n</font> is <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">convergent</a> &amp;  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>

<b>thus </b><a NAME="E3:47_1_1_1"/>
( <font color="Maroon" title="c3">h</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Maroon" title="c4">n</font> is <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">convergent</a> &amp;  <a href="comseq_2.html#K2" title="COMSEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="txt" href="#E1:47_1_1_1"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="cfcont_1.html#T43" title="CFCONT_1:th.43">CFCONT_1:43</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="E2:47_1_1"/>
<font color="Maroon" title="c3">h</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> <font color="Maroon" title="c4">n</font> is <a href="cfdiff_1.html#V1" title="CFDIFF_1:attr.1">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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