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<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">well-unital</a> <a href="algstr_1.html#V9" title="ALGSTR_1:attr.9">almost_invertible</a> <a href="algstr_1.html#V10" title="ALGSTR_1:attr.10">almost_cancelable</a>  <a href="vectsp_1.html#L2" title="VECTSP_1:struct.2">multLoopStr_0</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>assume </b><a NAME="E1:71"/><i><font color="Green" title="E55">A1</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">G</font>
 ;<br/>

<b>hence </b><a NAME="E2:71"/><i><font color="Green" title="E56">A2</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_1.html#K7" title="ALGSTR_1:func.7">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="algstr_1.html#D25" target="_self" title="ALGSTR_1:def.25">Def25</a></i>;<br/>

<b>consider </b><font color="Maroon" title="c3">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E4:71"/><i><font color="Green" title="E57">A3</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="algstr_1.html#E1:71"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="algstr_1.html#D22" target="_self" title="ALGSTR_1:def.22">Def22</a></i>;<br/>
<a NAME="E5:71"/>
<font color="Maroon" title="c3">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_1.html#K7" title="ALGSTR_1:func.7">"</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_1.html#K7" title="ALGSTR_1:func.7">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="algstr_1.html#E4:71"><i><font color="Green" title="E57">A3</font></i></a>, <a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>;<br/>
<a NAME="E6:71"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_1.html#K7" title="ALGSTR_1:func.7">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="algstr_1.html#E2:71"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="vectsp_1.html#D13" title="VECTSP_1:def.13">VECTSP_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E7:71"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="algstr_1.html#K7" title="ALGSTR_1:func.7">"</a> </span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="algstr_1.html#E4:71"><i><font color="Green" title="E57">A3</font></i></a>, <a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>;<br/>


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