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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#L1" title="GROUP_1:struct.1">HGrStr</a> ;<br/>

<b>assume </b><a NAME="E1:34_1_1"/>
( <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> &amp; <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">Group-like</a> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c2">G</font> = <font color="Maroon" title="c1">G</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="group_1.html#V3" title="GROUP_1:attr.3">Group-like</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a>  <a href="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a>  ;<br/>
<a NAME="E3:34_1_1"/>
( <font color="Maroon" title="c2">G</font> is <a href="group_1.html#V2" title="GROUP_1:attr.2">unital</a> &amp; <font color="Maroon" title="c2">G</font> is <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">G</font>) <a href="finseqop.html#NR2" title="FINSEQOP:NR.2">has_an_inverseOp</a>  )
 
<b>by </b><i><a class="ref" href="group_1.html#T36" title="GROUP_1:th.36">GROUP_1:36</a></i>;<br/>
<b>hence </b><a NAME="E4:34_1_1"/>
<font color="Maroon" title="c1">G</font> is <a href="monoid_0.html#V13" title="MONOID_0:attr.13">invertible</a>
 <b>by </b><i><a class="ref" href="monoid_0.html#T17" target="_self" title="MONOID_0:th.17">Th17</a></i>;<br/>


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