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

<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">seq</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">r</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b2">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  ex <font color="Olive" title="b3">m</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 <br/>for <font color="Olive" title="b4">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 <font color="Olive" title="b4">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b3">m</font> holds <br/><span class="p1"><a href="csspace.html#K13" title="CSSPACE:func.13">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Olive" title="b4">n</font></span>)</span></span><a href="csspace.html#K13" title="CSSPACE:func.13">.||</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b2">r</font> &amp; <font color="Olive" title="b1">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  holds <br/> <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Olive" title="b1">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">seq</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">r</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  ex <font color="Olive" title="b2">m</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 <br/>for <font color="Olive" title="b3">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 <font color="Olive" title="b3">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b2">m</font> holds <br/><span class="p1"><a href="csspace.html#K13" title="CSSPACE:func.13">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Olive" title="b3">n</font></span>)</span></span><a href="csspace.html#K13" title="CSSPACE:func.13">.||</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b1">r</font> &amp; <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  holds <br/> <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</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="c3">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  ex <font color="Olive" title="b1">m</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 <br/>for <font color="Olive" title="b2">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 <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b1">m</font> holds <br/><span class="p1"><a href="csspace.html#K13" title="CSSPACE:func.13">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Olive" title="b2">n</font></span>)</span></span><a href="csspace.html#K13" title="CSSPACE:func.13">.||</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">r</font> &amp; <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  implies  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:33"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c3">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( for <font color="Olive" title="b1">m</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>   ex <font color="Olive" title="b2">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 <br/>( <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b1">m</font> &amp; not <span class="p1"><a href="csspace.html#K13" title="CSSPACE:func.13">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Olive" title="b2">n</font></span>)</span></span><a href="csspace.html#K13" title="CSSPACE:func.13">.||</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">r</font> ) or  not <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  or  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<span class="kw">given </span><font color="Maroon" title="c4">m</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> <span class="kw"> such that </span><a NAME="E3:33"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
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 <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c4">m</font> holds <br/><span class="p1"><a href="csspace.html#K13" title="CSSPACE:func.13">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Olive" title="b1">n</font></span>)</span></span><a href="csspace.html#K13" title="CSSPACE:func.13">.||</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">r</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  or  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:33_1_1"/>
(  not <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  or <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:33_1_1_1"/>
not <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  or  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:33_1_1_1"/>
(  not <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  or  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> )
 ; <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><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:33_1_1_2"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  or  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> )</span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:33_1_1_2_1"/>
 <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">X</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">k</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> <span class="kw"> such that </span><br/><a NAME="E3:33_1_1_2_1"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
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 <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c5">k</font> holds <br/><span class="p1"><a href="csspace.html#K13" title="CSSPACE:func.13">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">X</font>)</span>)</span></span><a href="csspace.html#K13" title="CSSPACE:func.13">.||</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E1:33_1_1_2"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="clvect_2.html#T19" title="CLVECT_2:th.19">CLVECT_2:19</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1_2_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">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="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font></span><br/><span class="kw">assume </span><a NAME="E1:33_1_1_2_1_1"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:33_1_1_2_1_1"/>
<font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c5">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E3:33_1_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c5">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_1_2_1_1"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E4:33_1_1_2_1_1"/><span class="kw">then </span>
<span class="p1"><a href="csspace.html#K13" title="CSSPACE:func.13">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c6">n</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">X</font>)</span>)</span></span><a href="csspace.html#K13" title="CSSPACE:func.13">.||</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33_1_1_2_1"><span class="lab"><font color="Green" title="E18">A4</font></span></a></span>;<br/><a NAME="E5:33_1_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<span class="p1"><a href="csspace.html#K13" title="CSSPACE:func.13">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span><a href="csspace.html#K13" title="CSSPACE:func.13">.||</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">r</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T26" title="RLVECT_1:th.26">RLVECT_1:26</a></span>;<br/><a NAME="E6:33_1_1_2_1_1"/>
<font color="Maroon" title="c4">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c5">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c4">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>;<br/><a NAME="E7:33_1_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c4">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33_1_1_2_1_1"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><span class="kw">hence </span><a NAME="E8:33_1_1_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:33"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:33_1_1_2_1_1"><span class="lab"><font color="Green" title="E20">A6</font></span></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><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:33_1_1_2_1"/>
contradiction
 ; <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><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:33_1_1_2"/>
(  not <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  or  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> )
 ; <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><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:33"/>
(  not <font color="Maroon" title="c2">seq</font> is  <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>  or  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c2">seq</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font> )
 ; <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>
