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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <a href="mod_2.html#K18" target="_self">Z3</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">0,1,2</span><a href="enumset1.html#K1">}</a></span>;<br/>



<b>assume </b><a NAME="E1:55"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<b>hence </b><font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> = 
<a href="mod_2.html#K13" target="_self">add3</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="mod_2.html#K11" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="mod_2.html#D18" target="_self">Def18</a></i>
;<br/><br/>

<b>thus </b><font color="Maroon">c<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font> = 
<a href="mod_2.html#K14" target="_self">mult3</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="mod_2.html#E1:55"><i><font color="Green">E42</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="mod_2.html#K12" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="mod_2.html#D19" target="_self">Def19</a></i>
;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="mod_2.html#K10" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <a href="mod_2.html#K18" target="_self">Z3</a>  ;<br/>
<font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c<sub>5</sub></font> = 
<a href="mod_2.html#K13" target="_self">add3</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="mod_2.html#K10" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="mod_2.html#E1:55"><i><font color="Green">E42</font></i></a>, <a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="mod_2.html#K11" target="_self">+</a> <span class="p1">(<span class="default"><a href="mod_2.html#K10" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="mod_2.html#D18" target="_self">Def18</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="mod_2.html#K18" target="_self">Z3</a> 
<b>by </b><i><a class="txt" href="mod_2.html#E65"><i><font color="Green">Lemma40</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E6:55"/>
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#K10" target="_self">-</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D10">RLVECT_1:def 10</a></i>;<br/>


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