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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:2_2_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">L</font> is <a href="rlvect_1.html#V3">Abelian</a>
 ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>thus </b>the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">L</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> = 
<font color="Maroon">a</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#D5">RLVECT_1:def 5</a></i>
<br/>.= 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">L</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:2_2_1"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds  the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">L</font> <a href="binop_1.html#K1">.</a> <font color="Olive">a</font>,<font color="Olive">b</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">L</font> <a href="binop_1.html#K1">.</a> <font color="Olive">b</font>,<font color="Olive">a</font>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D5">RLVECT_1:def 5</a><br/>

<b>thus </b><font color="Maroon">a</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">b</font> = 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">L</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">L</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">b</font>,<font color="Maroon">a</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
;<br/>


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