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<b>let </b><font color="Maroon">G</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/>

<b>assume </b><a NAME="E1:35_5_1"/>
( <font color="Maroon">G</font> is <a href="group_1.html#V4">associative</a> &amp; <font color="Maroon">G</font> is <a href="monoid_0.html#V13" target="_self">invertible</a> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">G</font> = <font color="Maroon">G</font> as  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V4">associative</a> <a href="monoid_0.html#V13" target="_self">invertible</a>  <a href="group_1.html#L1">HGrStr</a>  ;<br/>
<a NAME="E3:35_5_1"/>
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>  st ( <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">c</font> or <font color="Olive">b</font> <a href="group_1.html#K1">*</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> <a href="group_1.html#K1">*</a> <font color="Olive">a</font> ) holds <br/><font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font>
 
<b>by </b><i><a class="ref" href="group_1.html#T14">GROUP_1:14</a></i>;<br/>
<b>hence </b><a NAME="E4:35_5_1"/>
( <font color="Maroon">G</font> is <a href="group_1.html#V2">unital</a> &amp; <font color="Maroon">G</font> is <a href="monoid_0.html#V16" target="_self">cancelable</a> )
 <b>by </b><i/>;<br/>


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