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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="comseq_1.html#NM1">Complex_Sequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="comseq_2.html#V1">bounded</a>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green">E15</font></i>: 
 <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p2"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="comseq_1.html#K9">.|</a></span></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E3:13"/><i><font color="Green">E16</font></i>: 
<span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="comseq_1.html#K9">.|</a></span> is <a href="seq_2.html#V3">bounded</a>
 
<b>by </b><i><a class="txt" href="csspace4.html#E1:13"><i><font color="Green">E14</font></i></a>, <a class="txt" href="csspace4.html#E11"><i><font color="Green">Lemma11</font></i></a></i>;<br/>
<a NAME="E4:13"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span>
 
<b>by </b><i><a class="ref" href="complex1.html#T132">COMPLEX1:132</a></i>;<br/>
<a NAME="E5:13"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="comseq_1.html#K9">.|</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="comseq_1.html#D14">COMSEQ_1:def 14</a></i>;<br/>
<a NAME="E6:13"/><b>then </b>
<span class="p1"><a href="comseq_1.html#K9">|.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="comseq_1.html#K9">.|</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="csspace4.html#E2:13"><i><font color="Green">E15</font></i></a>, <a class="txt" href="csspace4.html#E3:13"><i><font color="Green">E16</font></i></a>, <a class="txt" href="csspace4.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E7:13"/><b>then </b>
<span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complex1.html#K17">.|</a></span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="comseq_1.html#D14">COMSEQ_1:def 14</a></i>;<br/>
<b>hence </b><a NAME="E8:13"/>
<font color="Maroon">c<sub>1</sub></font> <a href="comseq_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="complex1.html#K5">0c</a> 
 <b>by </b><i><a class="ref" href="complex1.html#T131">COMPLEX1:131</a></i>;<br/>


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