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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V8">left_unital</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<a NAME="E1:75"/><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="vectsp_1.html#K7">comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D25">VECTSP_1:def 25</a></i>;<br/>
<a NAME="E2:75"/><i><font color="Green">E39</font></i>: 
(  <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  )
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T7" target="_self">Th7</a>, <a class="ref" href="fvsum_1.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E3:75"/><i><font color="Green">E40</font></i>: 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#R6">is_distributive_wrt</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E4:75"/><i><font color="Green">E41</font></i>: 
( the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="setwiseo.html#NR1" target="_self">has_a_unity</a>  &amp; the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finseqop.html#NR2" target="_self">has_an_inverseOp</a>  &amp;  <a href="finseqop.html#K6">the_inverseOp_wrt</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a>  <a href="vectsp_1.html#K7">comp</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T10" target="_self">Th10</a>, <a class="ref" href="fvsum_1.html#T17" target="_self">Th17</a>, <a class="ref" href="fvsum_1.html#T18" target="_self">Th18</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="fvsum_1.html#K10" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default">the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funcop_1.html#K8">[;]</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font>

<br/>.= 
<span class="p1">(<span class="default"><a href="vectsp_1.html#K7">comp</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="fvsum_1.html#E1:75"><i><font color="Green">E38</font></i></a>, <a class="txt" href="fvsum_1.html#E2:75"><i><font color="Green">E39</font></i></a>, <a class="txt" href="fvsum_1.html#E3:75"><i><font color="Green">E40</font></i></a>, <a class="txt" href="fvsum_1.html#E4:75"><i><font color="Green">E41</font></i></a>, <a class="ref" href="finseqop.html#T72">FINSEQOP:72</a></i>
<br/>.= 
 <a href="fvsum_1.html#K6" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font>

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