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<b>let </b><font color="Maroon">A</font> be  <a href="integra1.html#V1">closed-interval</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_1_1"/>
(  <a href="integra1.html#K3">vol</a> <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or  <a href="integra1.html#K3">vol</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1_1"><b>suppose </b></a><a NAME="E1:17_1_1_1"/><i><font color="Green">E38</font></i>: 
 <a href="integra1.html#K3">vol</a> <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:17_1_1_1"/>
 <a href="integra1.html#K3">vol</a> <font color="Maroon">A</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="integra1.html#T11">INTEGRA1:11</a></i>;<br/><b>hence </b><a NAME="E3:17_1_1_1"/>
 ex <font color="Olive">T</font> being  <a href="integra2.html#NM1">DivSequence</a> of <font color="Maroon">A</font> st <br/>(  <a href="integra2.html#K2">delta</a> <font color="Olive">T</font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="integra2.html#K2">delta</a> <font color="Olive">T</font></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1_2"><b>suppose </b></a><a NAME="E1:17_1_1_2"/>
 <a href="integra1.html#K3">vol</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:17_1_1_2"/>
 ex <font color="Olive">T</font> being  <a href="integra2.html#NM1">DivSequence</a> of <font color="Maroon">A</font> st <br/>(  <a href="integra2.html#K2">delta</a> <font color="Olive">T</font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="integra2.html#K2">delta</a> <font color="Olive">T</font></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:17"/>
 ex <font color="Olive">T</font> being  <a href="integra2.html#NM1">DivSequence</a> of <font color="Maroon">A</font> st <br/>(  <a href="integra2.html#K2">delta</a> <font color="Olive">T</font> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="integra2.html#K2">delta</a> <font color="Olive">T</font></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>


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