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<b>let </b><font color="Maroon">e1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> , <font color="Maroon">e2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <a href="vectsp_1.html#K3">F_Real</a> , <font color="Maroon">f2</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <a href="vectsp_1.html#K3">F_Real</a> ;<br/>



<b>assume </b><a NAME="E1:44"/><i><font color="Green">E43</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e2</font> &amp; <font color="Maroon">e1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> &amp; <font color="Maroon">e2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> )
 ;<br/>

<b>set </b><font color="Maroon">l</font> =  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font>;<br/>
<b>set </b><font color="Maroon">Y</font> = <span class="p1">{<span class="default"> <font color="Olive">e</font> where <font color="Olive">e</font> is    <a href="finseq_2.html#M2">Element</a> of <a href="numbers.html#K1">REAL</a>  <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font> </span>}</span> ;<br/>
<b>set </b><font color="Maroon">Z</font> = <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="vectsp_1.html#K3">F_Real</a>  <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font> </span>}</span> ;<br/>
<b>reconsider </b><font color="Maroon">e3</font> = <font color="Maroon">e1</font> as    <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T110">FINSEQ_2:110</a></i>;<br/>
<a NAME="E3:44"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font> &amp; <font color="Maroon">e2</font> is    <a href="finseq_2.html#M2">Element</a> of <a href="numbers.html#K1">REAL</a>  <a href="finseq_2.html#K3">*</a>  )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E4:44"/><b>then </b>
<font color="Maroon">e2</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">e</font> where <font color="Olive">e</font> is    <a href="finseq_2.html#M2">Element</a> of <a href="numbers.html#K1">REAL</a>  <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font> </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon">e4</font> = <font color="Maroon">e2</font> as    <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="finseq_2.html#D4">FINSEQ_2:def 4</a></i>;<br/>
<a NAME="E6:44"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font> &amp; <font color="Maroon">f1</font> is    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="vectsp_1.html#K3">F_Real</a>  <a href="finseq_2.html#K3">*</a>  )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E7:44"/><b>then </b>
<font color="Maroon">f1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="vectsp_1.html#K3">F_Real</a>  <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font> </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon">f3</font> = <font color="Maroon">f1</font> as    <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <a href="vectsp_1.html#K3">F_Real</a>  <b>by </b><i><a class="ref" href="finseq_2.html#D4">FINSEQ_2:def 4</a></i>;<br/>
<a NAME="E9:44"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font> &amp; <font color="Maroon">f2</font> is    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="vectsp_1.html#K3">F_Real</a>  <a href="finseq_2.html#K3">*</a>  )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E10:44"/><b>then </b>
<font color="Maroon">f2</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="vectsp_1.html#K3">F_Real</a>  <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font> </span>}</span> 
 
;<br/>
<b>then reconsider </b><font color="Maroon">f4</font> = <font color="Maroon">f2</font> as    <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">e1</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <a href="vectsp_1.html#K3">F_Real</a>  <b>by </b><i><a class="ref" href="finseq_2.html#D4">FINSEQ_2:def 4</a></i>;<br/>
<a NAME="E12:44"/>
 <a href="rvsum_1.html#K14">mlt</a> <font color="Maroon">e3</font>,<font color="Maroon">e4</font> <a href="hidden.html#R1">=</a>  <a href="fvsum_1.html#K12">mlt</a> <font color="Maroon">f3</font>,<font color="Maroon">f4</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E13:44"/>
 <a href="rvsum_1.html#K13">mlt</a> <font color="Maroon">e1</font>,<font color="Maroon">e2</font> <a href="hidden.html#R1">=</a>  <a href="fvsum_1.html#K11">mlt</a> <font color="Maroon">f1</font>,<font color="Maroon">f2</font>
 ;<br/>


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