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<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="116_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="116_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:116_1_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_001.html#K3" target="_self">.first()</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_001.html#K3" target="_self">.first()</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="116_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:116_1_1_1_1_1"/><i><font color="Green">E104</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_001.html#K3" target="_self">.first()</a> 
 ;<br/><div class="add"><a NAME="E2:116_1_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> 
 <b>by </b><i><a class="ref" href="glib_001.html#D24" target="_self">Def24</a></i>;<br/><b>then </b><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K3" target="_self">.first()</a>  = 
<font color="Maroon">c<sub>3</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a> 
<b>by </b><i><a class="ref" href="glib_001.html#D24" target="_self">Def24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K4" target="_self">.last()</a> 
<b>by </b><i><a class="txt" href="glib_001.html#E1:116_1_1_1_1_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="glib_001.html#E52"><i><font color="Green">Lemma44</font></i></a></i>
;<br/><a NAME="E4:116_1_1_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K3" target="_self">.first()</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="glib_001.html#K4" target="_self">.last()</a> 
 <b>by </b><i><a class="txt" href="glib_001.html#E1:116_1_1_1_1_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="glib_001.html#E52"><i><font color="Green">Lemma44</font></i></a></i>;<br/><b>hence </b><a NAME="E5:116_1_1_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V1" target="_self">closed</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D24" target="_self">Def24</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="116_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:116_1_1_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K4" target="_self">.last()</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="glib_001.html#K3" target="_self">.first()</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:116_1_1_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V1" target="_self">closed</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D10" target="_self">Def10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:116_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="glib_001.html#K7" target="_self">.append</a> <font color="Maroon">c<sub>3</sub></font> is <a href="glib_001.html#V1" target="_self">closed</a>
 ;<br/>


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