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<b>let </b><font color="Maroon">H</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="monoid_0.html#M2" target="_self">SubStr</a> of <font color="Maroon">G</font>;<br/>

<b>assume </b><a NAME="E1:106_1_1"/>
( <font color="Maroon">H</font> is <a href="group_1.html#V4">associative</a> &amp; <font color="Maroon">H</font> is <a href="monoid_0.html#V13" target="_self">invertible</a> )
 ;<br/>

<a NAME="E2:106_1_1"/><b>then </b>
<font color="Maroon">H</font> is  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/>
<b>hence </b><a NAME="E3:106_1_1"/>
( <font color="Maroon">H</font> is <a href="group_1.html#V2">unital</a> &amp; <font color="Maroon">H</font> is <a href="monoid_0.html#V16" target="_self">cancelable</a> &amp; <font color="Maroon">H</font> is <a href="group_1.html#V3">Group-like</a> )
 ;<br/>


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