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<b>let </b><font color="Maroon">c<sub>1</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="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" target="_self">opp</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:10"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font> = 
the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" target="_self">opp</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="mod_4.html#E1:10"><i><font color="Green">E7</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>5</sub></font>

;<br/>

<b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> = 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>

<br/>.= 
the <a href="group_1.html#U1">mult</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" target="_self">opp</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="mod_4.html#E1:10"><i><font color="Green">E7</font></i></a>, <a class="ref" href="mod_4.html#T1" target="_self">Th1</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font>

;<br/>

<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> = 
the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" target="_self">opp</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K1">]</a></span>
<b>by </b><i><a class="txt" href="mod_4.html#E1:10"><i><font color="Green">E7</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>4</sub></font>

<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><a href="mod_4.html#K2" target="_self">opp</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<b>hence </b><a NAME="E6:10"/>
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T19">RLVECT_1:19</a></i>;<br/>


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