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<b>let </b><font color="Maroon" title="c1">seq</font> be   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>;<br/>

<b>assume </b><a NAME="E1:87"/><i><font color="Green" title="E54">A1</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="87_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">r</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><a NAME="E1:87_1"/>
<font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c1">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 <b>by </b><i><a class="txt" href="seqm_3.html#E1:87"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="seqm_3.html#T65" target="_self" title="SEQM_3:th.65">Th65</a></i>;<br/><b>hence </b><a NAME="E2:87_1"/>
<font color="Maroon" title="c2">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#T73" target="_self" title="SEQM_3:th.73">Th73</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:87"/>
for <font color="Olive" title="b1">r</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  holds  <font color="Olive" title="b1">r</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 ;<br/>

<a NAME="E4:87"/>
 <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c1">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E1:87"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="seqm_3.html#T65" target="_self" title="SEQM_3:th.65">Th65</a></i>;<br/>
<b>hence </b><a NAME="E5:87"/>
 <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#T73" target="_self" title="SEQM_3:th.73">Th73</a></i>;<br/>

<a NAME="E6:87"/>
 <a href="valued_1.html#K56" title="VALUED_1:func.56">abs</a> <font color="Maroon" title="c1">seq</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 
<b>by </b><i><a class="txt" href="seqm_3.html#E1:87"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="seqm_3.html#T65" target="_self" title="SEQM_3:th.65">Th65</a></i>;<br/>
<b>hence </b><a NAME="E7:87"/>
 <a href="valued_1.html#K56" title="VALUED_1:func.56">abs</a> <font color="Maroon" title="c1">seq</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 <b>by </b><i><a class="ref" href="seqm_3.html#T73" target="_self" title="SEQM_3:th.73">Th73</a></i>;<br/>


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