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<b>let </b><font color="Maroon">G</font> be  <a href="vectsp_1.html#V5">left-distributive</a> <a href="algstr_2.html#NM1">doubleLoop</a>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/>





<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_2.html#K1" target="_self">-</a> <font color="Maroon">b</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="rlvect_1.html#K2">+</a> <span class="p2">(<span class="default"><a href="algstr_2.html#K1" target="_self">-</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#D12">VECTSP_1:def 12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">G</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font>
<b>by </b><i><a class="txt" href="algstr_2.html#E1"><i><font color="Green">Lemma9</font></i></a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">G</font>
<b>by </b><i><a class="ref" href="algstr_1.html#T34">ALGSTR_1:34</a></i>
;<br/>
<b>hence </b><a NAME="E2:17"/>
<span class="p1">(<span class="default"><a href="algstr_2.html#K1" target="_self">-</a> <font color="Maroon">b</font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="algstr_2.html#K1" target="_self">-</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i><a class="txt" href="algstr_2.html#E1"><i><font color="Green">Lemma9</font></i></a></i>;<br/>


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