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

<span class="kw">let </span><font color="Maroon" title="c1">s</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">s</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a>  implies ( <font color="Maroon" title="c1">s</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="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:7"/>
<font color="Maroon" title="c1">s</font> is  <a href="series_1.html#V1" title="SERIES_1:attr.1">summable</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">s</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="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>

<a NAME="E2:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A1</font></span>: 
 <a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="series_1.html#D2" target="_self" title="SERIES_1:def.2">Def2</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">n</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span><br/><a NAME="E1:7_1"/>
<span class="p1">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="series_1.html#D1" target="_self" title="SERIES_1:def.1">Def1</a></span>;<br/><a NAME="E2:7_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#D3" title="NAT_1:def.3">NAT_1:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:7_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#D3" title="NAT_1:def.3">NAT_1:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E4:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A2</font></span>: 
<span class="p1">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_1.html#T7" title="SEQ_1:th.7">SEQ_1:7</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">n</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p3">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p3">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <span class="p3">(<span class="default"><a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <span class="p4">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_1.html#T7" title="SEQ_1:th.7">SEQ_1:7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <span class="p4">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_1.html#T7" title="SEQ_1:th.7">SEQ_1:7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_1.html#T10" title="SEQ_1:th.10">SEQ_1:10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">n</font>

; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E6:7"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" title="FUNCT_2:th.63">FUNCT_2:63</a></span>;<br/>
<a NAME="E7:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A3</font></span>: 
<font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:7"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="seq_1.html#T31" title="SEQ_1:th.31">SEQ_1:31</a></span>;<br/>
<a NAME="E8:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E11">A4</font></span>: 
<font color="Maroon" title="c1">s</font> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1 is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E8">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:7"/>
<font color="Maroon" title="c1">s</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#T21" title="SEQ_4:th.21">SEQ_4:21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/>

<a NAME="E10:7"/>
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="seq_4.html#T20" title="SEQ_4:th.20">SEQ_4:20</a></span>;<br/>
<span class="kw">then </span> <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span> <a href="valued_0.html#K1" title="VALUED_0:func.1">^\</a> 1</span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p2">(<span class="default"><a href="series_1.html#K2" title="SERIES_1:func.2">Partial_Sums</a> <font color="Maroon" title="c1">s</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="seq_2.html#T12" title="SEQ_2:th.12">SEQ_2:12</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/>
<span class="kw">hence </span><a NAME="E12:7"/>
 <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c1">s</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">by</span> <span class="lab"><a class="txt" href="#E7:7"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="txt" href="#E8:7"><span class="lab"><font color="Green" title="E11">A4</font></span></a>, <a class="ref" href="seq_4.html#T22" title="SEQ_4:th.22">SEQ_4:22</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
