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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">G</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">H</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="monoid_0.html#M2" title="MONOID_0:mode.2">SubStr</a> of <font color="Maroon" title="c2">G</font>;<br/>





<a NAME="E1:42"/>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">H</font>) <a href="funct_4.html#NR1" title="FUNCT_4:NR.1">&lt;=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">G</font>) &amp; <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_1.html#K9" title="MONOID_1:func.9">.:</a> <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c1">X</font>) <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">G</font>),<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">G</font>) <a href="monoid_1.html#K8" title="MONOID_1:func.8">.:</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_1.html#K9" title="MONOID_1:func.9">.:</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c1">X</font>) <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">H</font>),<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c3">H</font>) <a href="monoid_1.html#K8" title="MONOID_1:func.8">.:</a> <font color="Maroon" title="c1">X</font> )
 
<b>by </b><i><a class="ref" href="monoid_1.html#T18" target="_self" title="MONOID_1:th.18">Th18</a>, <a class="ref" href="monoid_0.html#D23" title="MONOID_0:def.23">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" title="MONOID_1:func.9">.:</a> <font color="Maroon" title="c3">H</font>,<font color="Maroon" title="c1">X</font>) <a href="funct_4.html#NR1" title="FUNCT_4:NR.1">&lt;=</a> <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_1.html#K9" title="MONOID_1:func.9">.:</a> <font color="Maroon" title="c2">G</font>,<font color="Maroon" title="c1">X</font>)
 <b>by </b><i><a class="ref" href="monoid_1.html#T17" target="_self" title="MONOID_1:th.17">Th17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="monoid_0.html#D23" title="MONOID_0:def.23">MONOID_0:def 23</a><br/>


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