<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp; <font color="Maroon" title="c1">G</font> is  <a href="group_1.html#V2" title="GROUP_1:attr.2">Group-like</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="monoid_0.html#V13" title="MONOID_0:attr.13">invertible</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:36_1_1"/>
( <font color="Maroon" title="c1">G</font> is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp; <font color="Maroon" title="c1">G</font> is  <a href="group_1.html#V2" title="GROUP_1:attr.2">Group-like</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G</font> is  <a href="monoid_0.html#V13" title="MONOID_0:attr.13">invertible</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><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#V2" title="GROUP_1:attr.2">Group-like</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a>  ;<br/>
<a NAME="E3:36_1_1"/>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">G</font>) is  <a href="finseqop.html#V1" title="FINSEQOP:attr.1">having_an_inverseOp</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#T36" title="GROUP_1:th.36">GROUP_1:36</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:36_1_1"/>
<font color="Maroon" title="c1">G</font> is  <a href="monoid_0.html#V13" title="MONOID_0:attr.13">invertible</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#T17" target="_self" title="MONOID_0:th.17">Th17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
