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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/>

<b>assume </b><a NAME="E1:35_5_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="group_1.html#V4">associative</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="monoid_0.html#V13" target="_self">invertible</a> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  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/>
<a NAME="E3:35_5_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> st ( <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>3</sub></font> or <font color="Olive">b<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font> ) holds <br/><font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="group_1.html#T14">GROUP_1:14</a></i>;<br/>
<b>hence </b><a NAME="E4:35_5_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="group_1.html#V2">unital</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="monoid_0.html#V16" target="_self">cancelable</a> )
 <b>by </b><i><a class="ref" href="monoid_0.html#T15" target="_self">Th15</a></i>;<br/>


</div>
