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

<b>set </b><font color="Maroon">seq1</font> =  <a href="rinfsup1.html#K3" target="_self">inferior_realsequence</a> <font color="Maroon">seq</font>;<br/>
<b>set </b><font color="Maroon">r1</font> =  <a href="rinfsup1.html#K1" target="_self">sup</a> <span class="p1">(<span class="default"><a href="rinfsup1.html#K3" target="_self">inferior_realsequence</a> <font color="Maroon">seq</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">r</font> =  <a href="rinfsup1.html#K2" target="_self">inf</a> <span class="p1">(<span class="default"><a href="rinfsup1.html#K4" target="_self">superior_realsequence</a> <font color="Maroon">seq</font></span>)</span>;<br/>
<b>assume </b><a NAME="E1:64"/>
<font color="Maroon">seq</font> is <a href="seq_2.html#V3">bounded</a>
 ;<br/>

<a NAME="E2:64"/><b>then </b>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="rinfsup1.html#K3" target="_self">inferior_realsequence</a> <font color="Maroon">seq</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rinfsup1.html#K2" target="_self">inf</a> <span class="p1">(<span class="default"><a href="rinfsup1.html#K4" target="_self">superior_realsequence</a> <font color="Maroon">seq</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rinfsup1.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E3:64"/>
 <a href="rinfsup1.html#K1" target="_self">sup</a> <span class="p1">(<span class="default"><a href="rinfsup1.html#K3" target="_self">inferior_realsequence</a> <font color="Maroon">seq</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rinfsup1.html#K2" target="_self">inf</a> <span class="p1">(<span class="default"><a href="rinfsup1.html#K4" target="_self">superior_realsequence</a> <font color="Maroon">seq</font></span>)</span>
 <b>by </b><i/>;<br/>


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