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<b>let </b><font color="Maroon">R</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<a NAME="E1:47"/>
0 <a href="rvsum_1.html#K9">*</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">0 <a href="rvsum_1.html#K2">multreal</a> </span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="rvsum_1.html#D7">RVSUM_1:def 7</a></i>;<br/>
<a NAME="E2:47"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default">0 <a href="rvsum_1.html#K9">*</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T37">FINSEQ_2:37</a></i>;<br/>
<a NAME="E3:47"/><i><font color="Green">E32</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">R</font></span>)</span> &amp;  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default">0 <a href="rvsum_1.html#K9">*</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default">0 <a href="rvsum_1.html#K9">*</a> <font color="Maroon">R</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E4:47"/>
<span class="p1">(<span class="default">0 <a href="rvsum_1.html#K9">*</a> <font color="Maroon">R</font></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">R</font>
 <b>by </b><i><a class="txt" href="rfinseq.html#E2:47"><i><font color="Green">E31</font></i></a>, <a class="ref" href="relat_1.html#T167">RELAT_1:167</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E5:47"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">R</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">i</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/>
<span class="p1">(<span class="default">0 <a href="rvsum_1.html#K9">*</a> <font color="Maroon">R</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font> = 
0 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T66">RVSUM_1:66</a></i>
<br/>.= 
0

;<br/>
<a NAME="E8:47"/><b>then </b>
<span class="p1">(<span class="default">0 <a href="rvsum_1.html#K9">*</a> <font color="Maroon">R</font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E9:47"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default">0 <a href="rvsum_1.html#K9">*</a> <font color="Maroon">R</font></span>)</span> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="rfinseq.html#E2:47"><i><font color="Green">E31</font></i></a>, <a class="txt" href="rfinseq.html#E3:47"><i><font color="Green">E32</font></i></a>, <a class="ref" href="rfinseq.html#T1" target="_self">Th1</a>, <a class="ref" href="funct_1.html#D13">FUNCT_1:def 13</a></i>;<br/>


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