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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">G</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/><b>let </b><font color="Maroon">H</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="monoid_0.html#M2">SubStr</a> of <font color="Maroon">G</font>;<br/>





<a NAME="E1:42"/>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H</font>) <a href="funct_4.html#NR1" target="_self">&lt;=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">G</font>) &amp; <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_1.html#K9" target="_self">.:</a> <font color="Maroon">G</font>,<font color="Maroon">X</font>) <a href="funct_2.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">G</font>),<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">G</font>) <a href="monoid_1.html#K8" target="_self">.:</a> <font color="Maroon">X</font> &amp; <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_1.html#K9" target="_self">.:</a> <font color="Maroon">H</font>,<font color="Maroon">X</font>) <a href="funct_2.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H</font>),<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">H</font>) <a href="monoid_1.html#K8" target="_self">.:</a> <font color="Maroon">X</font> )
 
<b>by </b><i>, <a class="ref" href="monoid_0.html#D23">MONOID_0:def 23</a></i>;<br/>
<b>hence </b><a NAME="E2:42"/>
<font color="Maroon">H<sub>1</sub></font>( <a href="monoid_1.html#K9" target="_self">.:</a> <font color="Maroon">H</font>,<font color="Maroon">X</font>) <a href="funct_4.html#NR1" target="_self">&lt;=</a> <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_1.html#K9" target="_self">.:</a> <font color="Maroon">G</font>,<font color="Maroon">X</font>)
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D23">MONOID_0:def 23</a><br/>


</div>
