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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:2_1_1_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">L</font> is <a href="rlvect_1.html#V4">add-associative</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>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><a NAME="E2:2_1_1_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">a</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">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="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/><a NAME="E3:2_1_1_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c</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="Maroon">b</font>,<font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>;<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> <span class="p1">(<span class="default">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></span>)</span>,<font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</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">a</font>,<span class="p1">(<span class="default">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">c</font></span>)</span>
<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_1_1"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</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> <span class="p1">(<span class="default">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></span>)</span>,<font color="Olive">c</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">a</font>,<span class="p1">(<span class="default">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">c</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon">u</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">v</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">w</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#D6">RLVECT_1:def 6</a><br/>

<a NAME="E3:2_1_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">u</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">v</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="Maroon">u</font>,<font color="Maroon">v</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>;<br/>
<a NAME="E4:2_1_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">v</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">w</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="Maroon">v</font>,<font color="Maroon">w</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">v</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">w</font> = 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">L</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default">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">u</font>,<font color="Maroon">v</font></span>)</span>,<font color="Maroon">w</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">u</font>,<span class="p1">(<span class="default">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">v</font>,<font color="Maroon">w</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">u</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">w</font></span>)</span>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
;<br/>


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