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<b>let </b><font color="Maroon" title="c2">H</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="monoid_0.html#M2" title="MONOID_0:mode.2">SubStr</a> of <font color="Maroon" title="c1">G</font>;<br/>

<b>assume </b><a NAME="E1:102_1_1"/>
( <font color="Maroon" title="c2">H</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a> &amp; <font color="Maroon" title="c2">H</font> is <a href="monoid_0.html#V13" title="MONOID_0:attr.13">invertible</a> )
 ;<br/>

<a NAME="E2:102_1_1"/><b>then </b>
<font color="Maroon" title="c2">H</font> is  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">associative</a> <a href="monoid_0.html#V13" title="MONOID_0:attr.13">invertible</a>  <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> 
 
;<br/>
<b>hence </b><a NAME="E3:102_1_1"/>
( <font color="Maroon" title="c2">H</font> is <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a> &amp; <font color="Maroon" title="c2">H</font> is <a href="monoid_0.html#V16" title="MONOID_0:attr.16">cancelable</a> &amp; <font color="Maroon" title="c2">H</font> is <a href="group_1.html#V2" title="GROUP_1:attr.2">Group-like</a> )
 ;<br/>


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