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<b>consider </b><font color="Maroon">R</font> being   <a href="vectsp_2.html#NM1">comRing</a>;<br/>
<b>take </b>
<font color="Maroon">R</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_3_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/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_3_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:2_3_1_1_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="rlvect_1.html#K4">+</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#K4">+</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#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</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#K4">+</a> <font color="Maroon">a</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">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#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</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#K4">+</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="E2:2_3_1_1"/>
( ( <font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c</font> implies <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) &amp; ( <font color="Maroon">b</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">a</font> implies <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:2_3_1"/>
<font color="Maroon">R</font> is <a href="binom.html#V1" target="_self">add-cancelable</a>
 <b>by </b><i/>;<br/>


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