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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#V3">Abelian</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="rlvect_1.html#L1">LoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</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="E1:97"/><i><font color="Green">E46</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> 
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E2:97"/><i><font color="Green">E47</font></i>: 
( 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#T17" target="_self">Th17</a>, <a class="ref" href="fvsum_1.html#T18" target="_self">Th18</a></i>;<br/>
<b>thus </b> <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K8" target="_self">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finsop_1.html#K2">$$</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="fvsum_1.html#K8" target="_self">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

<br/>.= 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finsop_1.html#K2">$$</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fvsum_1.html#K2" target="_self">diffield</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseqop.html#K1">.:</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K2" target="_self">diffield</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default">the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finsop_1.html#K2">$$</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default">the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finsop_1.html#K2">$$</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="fvsum_1.html#E1:97"><i><font color="Green">E46</font></i></a>, <a class="txt" href="fvsum_1.html#E2:97"><i><font color="Green">E47</font></i></a>, <a class="ref" href="setwop_2.html#T48">SETWOP_2:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K2" target="_self">diffield</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default">the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finsop_1.html#K2">$$</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="fvsum_1.html#K2" target="_self">diffield</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T14" target="_self">Th14</a></i>
;<br/>


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