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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="csspace.html#K1" target="_self">the_set_of_ComplexSequences</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:8_1_2"/><i><font color="Green">E8</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default"><a href="csspace.html#K2" target="_self">seq_id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K5">0c</a> 
 <b>and </b><br/><a NAME="E2:8_1_2"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default"><a href="csspace.html#K2" target="_self">seq_id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K5">0c</a> 
 ;<br/>

<a NAME="E3:8_1_2"/><i><font color="Green">E10</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default"><a href="csspace.html#K2" target="_self">seq_id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="csspace.html#K2" target="_self">seq_id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E1:8_1_2_1"/>
<span class="p1">(<span class="default"><a href="csspace.html#K2" target="_self">seq_id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K5">0c</a> 
 
<b>by </b><i><a class="txt" href="csspace.html#E2:8_1_2"><i><font color="Green">E9</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:8_1_2_1"/>
<span class="p1">(<span class="default"><a href="csspace.html#K2" target="_self">seq_id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="csspace.html#K2" target="_self">seq_id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="csspace.html#E1:8_1_2"><i><font color="Green">E8</font></i></a></i>;<br/>


</div><b>end;</b></div>
<font color="Maroon">c<sub>1</sub></font> = 
 <a href="csspace.html#K2" target="_self">seq_id</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="csspace.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="csspace.html#K2" target="_self">seq_id</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="csspace.html#E3:8_1_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="comseq_1.html#T6">COMSEQ_1:6</a></i>
;<br/>
<b>hence </b><a NAME="E5:8_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="csspace.html#D2" target="_self">Def2</a></i>;<br/>


</div>
