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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="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="monoid_0.html#V13" title="MONOID_0:attr.13">invertible</a> implies ( <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a> &amp; <font color="Maroon" title="c1">G</font> is <a href="monoid_0.html#V16" title="MONOID_0:attr.16">cancelable</a> ) )</span><br/>

<b>assume </b><a NAME="E1:35_5_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="monoid_0.html#V13" title="MONOID_0:attr.13">invertible</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a> &amp; <font color="Maroon" title="c1">G</font> is <a href="monoid_0.html#V16" title="MONOID_0:attr.16">cancelable</a> )</span><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">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/>
<a NAME="E3:35_5_1"/>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font>  st ( <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">c</font> or <font color="Olive" title="b2">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">a</font> ) holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font>
 
<b>by </b><i><a class="ref" href="group_1.html#T14" title="GROUP_1:th.14">GROUP_1:14</a></i>;<br/>
<b>hence </b><a NAME="E4:35_5_1"/>
( <font color="Maroon" title="c1">G</font> is <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a> &amp; <font color="Maroon" title="c1">G</font> is <a href="monoid_0.html#V16" title="MONOID_0:attr.16">cancelable</a> )
 <b>by </b><i><a class="ref" href="monoid_0.html#T15" target="_self" title="MONOID_0:th.15">Th15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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