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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V2">unital</a> <a href="group_1.html#V4">associative</a> <a href="algstr_1.html#V9" target="_self">almost_invertible</a> <a href="algstr_1.html#V10" target="_self">almost_cancelable</a>  <a href="vectsp_1.html#L2">multLoopStr_0</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:75"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>hence </b><a NAME="E2:75"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="algstr_1.html#K7" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="algstr_1.html#D25" target="_self">Def25</a></i>;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:75"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="algstr_1.html#E1:75"><i><font color="Green">E60</font></i></a>, <a class="ref" href="algstr_1.html#D22" target="_self">Def22</a></i>;<br/>
<a NAME="E5:75"/>
<font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="algstr_1.html#K7" target="_self">"</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="algstr_1.html#K7" target="_self">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="algstr_1.html#E4:75"><i><font color="Green">E62</font></i></a>, <a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>;<br/>
<a NAME="E6:75"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="algstr_1.html#K7" target="_self">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="algstr_1.html#E2:75"><i><font color="Green">E61</font></i></a>, <a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E7:75"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="algstr_1.html#K7" target="_self">"</a> </span>)</span> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="algstr_1.html#E4:75"><i><font color="Green">E62</font></i></a>, <a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>;<br/>


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