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

<b>assume </b><a NAME="E1:29"/><i><font color="Green">E34</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> 3 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> 3 )
 ;<br/>

<a NAME="E2:29"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 3</span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>
 <a href="rvsum_1.html#K13">mlt</a> <font color="Maroon">f1</font>,<font color="Maroon">f2</font> = 
<a href="binop_2.html#K35">multreal</a>  <a href="finseqop.html#K1">.:</a> <font color="Maroon">f1</font>,<font color="Maroon">f2</font>
<b>by </b><i><a class="ref" href="rvsum_1.html#D9">RVSUM_1:def 9</a></i>
<br/>.= 
<a href="binop_2.html#K35">multreal</a>  <a href="finseqop.html#K1">.:</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 3</span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>,<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 3</span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="binop_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 1</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="binop_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="binop_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 3</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 3</span>)</span></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_2.html#T90">FINSEQ_2:90</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 1</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="binop_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 2</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="binop_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 3</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 3</span>)</span></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="binop_2.html#D11">BINOP_2:def 11</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 1</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 2</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="binop_2.html#K35">multreal</a>  <a href="binop_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 3</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 3</span>)</span></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="binop_2.html#D11">BINOP_2:def 11</a></i>
;<br/>
<b>hence </b><a NAME="E4:29"/>
 <a href="rvsum_1.html#K13">mlt</a> <font color="Maroon">f1</font>,<font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 1</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 2</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 2</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K2">.</a> 3</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="seq_1.html#K2">.</a> 3</span>)</span></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="binop_2.html#D11">BINOP_2:def 11</a></i>;<br/>


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