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<b>set </b><font color="Maroon">M</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Olive">s</font></span>)</span> where <font color="Olive">s</font> is    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> : for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">s</font> holds <br/> ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <br/>( <font color="Olive">s</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> ) </span>}</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="123_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:123_1_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Olive">s</font></span>)</span> where <font color="Olive">s</font> is    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> : for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">s</font> holds <br/> ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <br/>( <font color="Olive">s</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">s</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font><b> such that </b><br/><a NAME="E3:123_1_1_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">s</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">s</font> holds <br/> ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <br/>( <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> ) ) )
 ;<br/><b>thus </b><a NAME="E4:123_1_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">M</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Olive">s</font></span>)</span> where <font color="Olive">s</font> is    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> : for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">s</font> holds <br/> ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <br/>( <font color="Olive">s</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> ) </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font> <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E3:123_1_1"/>
<font color="Maroon">M</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>
 
;<br/>
<b>hence </b><a NAME="E4:123_1_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Olive">s</font></span>)</span> where <font color="Olive">s</font> is    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> : for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">s</font> holds <br/> ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> st <br/>( <font color="Olive">s</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font> ) </span>}</span>  is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>
 ;<br/>


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