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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a> <a href="vectsp_1.html#V1" title="VECTSP_1:attr.1">right-distributive</a> <a href="algstr_2.html#NM1" title="ALGSTR_2:NM.1">doubleLoop</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/>



<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D11" title="VECTSP_1:def.11">VECTSP_1:def 11</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">G</font></span>)</span>
<b>by </b><i><a class="ref" href="algstr_2.html#D7" target="_self" title="ALGSTR_2:def.7">Def7</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">G</font>
<b>by </b><i><a class="ref" href="algstr_1.html#T34" title="ALGSTR_1:th.34">ALGSTR_1:34</a></i>
;<br/>
<b>hence </b><a NAME="E2:10"/>
<font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_2.html#K1" title="ALGSTR_2:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="algstr_2.html#D7" target="_self" title="ALGSTR_2:def.7">Def7</a></i>;<br/>


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