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<b>let </b><font color="Maroon">x</font> be   <a href="vectsp_1.html#NM3">Scalar</a> of <a href="mod_2.html#K18" target="_self">Z3</a> , <font color="Maroon">y</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">X</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>, <font color="Maroon">Y</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">E29</font></i>: 
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 ;<br/>

<b>hence </b><font color="Maroon">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">y</font> = 
<a href="mod_2.html#K13" target="_self">add3</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
<font color="Maroon">X</font> <a href="mod_2.html#K11" target="_self">+</a> <font color="Maroon">Y</font>
<b>by </b><i/>
;<br/><br/>

<b>thus </b><a NAME="E3:55"/>
<font color="Maroon">x</font> <a href="group_1.html#K1">*</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="mod_2.html#K12" target="_self">*</a> <font color="Maroon">Y</font>
 <b>by </b><i>, </i>;<br/>

<b>reconsider </b><font color="Maroon">a</font> =  <a href="mod_2.html#K10" target="_self">-</a> <font color="Maroon">X</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">x</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">a</font> = 
<a href="mod_2.html#K13" target="_self">add3</a>  <a href="binop_1.html#K2">.</a> <font color="Maroon">X</font>,<span class="p1">(<span class="default"><a href="mod_2.html#K10" target="_self">-</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
<font color="Maroon">X</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">X</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="mod_2.html#K18" target="_self">Z3</a> 
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E6:55"/>
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#K10" target="_self">-</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D10">RLVECT_1:def 10</a></i>;<br/>


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