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<b>let </b><font color="Maroon">K</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">K</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">K</font>, <font color="Maroon">z</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">K</font>;<br/>



<b>assume </b><a NAME="E1:55"/><i><font color="Green">E29</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">x2</font> = <font color="Maroon">x</font>, <font color="Maroon">y2</font> = <font color="Maroon">y</font>, <font color="Maroon">z2</font> = <font color="Maroon">z</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> <b>by </b><i><a class="ref" href="finseq_2.html#T110">FINSEQ_2:110</a></i>;<br/>
 <a href="fvsum_1.html#K11">mlt</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="fvsum_1.html#K3">+</a> <font color="Maroon">y</font></span>)</span> = 
 <a href="fvsum_1.html#K12">mlt</a> <span class="p1">(<span class="default"><font color="Maroon">x2</font> <a href="fvsum_1.html#K4">+</a> <font color="Maroon">y2</font></span>)</span>,<font color="Maroon">z2</font>
<b>by </b><i><a class="ref" href="fvsum_1.html#T77">FVSUM_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K12">mlt</a> <font color="Maroon">x2</font>,<font color="Maroon">z2</font></span>)</span> <a href="fvsum_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K11">mlt</a> <font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K11">mlt</a> <font color="Maroon">z</font>,<font color="Maroon">x</font></span>)</span> <a href="fvsum_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12">mlt</a> <font color="Maroon">y2</font>,<font color="Maroon">z2</font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T77">FVSUM_1:77</a></i>
;<br/>
<b>hence </b><a NAME="E4:55"/>
 <a href="fvsum_1.html#K11">mlt</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="fvsum_1.html#K3">+</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K11">mlt</a> <font color="Maroon">z</font>,<font color="Maroon">x</font></span>)</span> <a href="fvsum_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K11">mlt</a> <font color="Maroon">z</font>,<font color="Maroon">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="fvsum_1.html#T77">FVSUM_1:77</a></i>;<br/>


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