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<b>let </b><font color="Maroon">ADG</font> be   <a href="tdgroup.html#NM2">Uniquely_Two_Divisible_Group</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">ADG</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">ADG</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">ADG</font>;<br/><b>let </b><font color="Maroon">b'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">ADG</font>;<br/>









<b>assume </b><a NAME="E1:21"/>
( <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="tdgroup.html#R1" target="_self">==&gt;</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b'</font> <a href="tdgroup.html#R1" target="_self">==&gt;</a> <font color="Maroon">b'</font>,<font color="Maroon">c</font> )
 ;<br/>

<a NAME="E2:21"/><b>then </b>
( <font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b'</font> )
 
<b>by </b><i/>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">b'</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon">b'</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b'</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">b'</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">b'</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">b'</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">b'</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">b'</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">ADG</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
<br/>.= 
<font color="Maroon">b'</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
;<br/>
<b>then </b><i><font color="Green">E19</font></i>: <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">b'</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">b'</font></span>)</span></span>)</span> = 
<font color="Maroon">b'</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">b'</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">ADG</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
;<br/>
<font color="Maroon">b'</font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">ADG</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b'</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">b'</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b'</font>
<b>by </b><i>, <a class="ref" href="vectsp_1.html#D28">VECTSP_1:def 28</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">b'</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b'</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">b</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">ADG</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
<br/>.= 
<font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E6:21"/>
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font>
 ;<br/>


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