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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:88"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V3">constant</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="88_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><a NAME="E1:88_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K14">(#)</a> <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V3">constant</a>
 <b>by </b><i><a class="txt" href="seqm_3.html#E1:88"><i><font color="Green">E55</font></i></a>, <a class="ref" href="seqm_3.html#T65" target="_self">Th65</a></i>;<br/><b>hence </b><a NAME="E2:88_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K14">(#)</a> <font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V3">bounded</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#T73" target="_self">Th73</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:88"/>
for <font color="Olive">b<sub>1</sub></font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  holds <font color="Olive">b<sub>1</sub></font> <a href="seq_1.html#K14">(#)</a> <font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V3">bounded</a>
 ;<br/>

<a NAME="E4:88"/>
 <a href="seq_1.html#K17">-</a> <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V3">constant</a>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E1:88"><i><font color="Green">E55</font></i></a>, <a class="ref" href="seqm_3.html#T65" target="_self">Th65</a></i>;<br/>
<b>hence </b><a NAME="E5:88"/>
 <a href="seq_1.html#K17">-</a> <font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V3">bounded</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#T73" target="_self">Th73</a></i>;<br/>

<a NAME="E6:88"/>
 <a href="seq_1.html#K22">abs</a> <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V3">constant</a>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E1:88"><i><font color="Green">E55</font></i></a>, <a class="ref" href="seqm_3.html#T65" target="_self">Th65</a></i>;<br/>
<b>hence </b><a NAME="E7:88"/>
 <a href="seq_1.html#K22">abs</a> <font color="Maroon">c<sub>1</sub></font> is <a href="seq_2.html#V3">bounded</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#T73" target="_self">Th73</a></i>;<br/>


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