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<b>let </b><font color="Maroon">R</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="rlvect_1.html#L1">LoopStr</a> ;<br/>

<b>assume </b><a NAME="E1:5_1_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">R</font> is <a href="rlvect_1.html#V5">right_zeroed</a> &amp; <font color="Maroon">R</font> is <a href="rlvect_1.html#V6">right_complementable</a> &amp; <font color="Maroon">R</font> is <a href="rlvect_1.html#V4">add-associative</a> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>, <font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>;<br/><b>assume </b><a NAME="E1:5_1_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">a</font>
 ;<br/><b>thus </b><font color="Maroon">b</font> = 
<font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K2">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon">c</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K2">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon">c</font> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">R</font></span>)</span>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
<br/>.= 
<font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:5_1_1"/>
<font color="Maroon">R</font> is <a href="algstr_1.html#V3">add-right-cancelable</a>
 <b>by </b><i><a class="ref" href="algstr_1.html#D7">ALGSTR_1:def 7</a></i>;<br/>


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