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<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" target="_self">SubStr</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>;<br/><b>let </b><font color="Maroon">a'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>, <font color="Maroon">b'</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/>







<b>assume </b><a NAME="E1:76"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font> )
 ;<br/>

<a NAME="E2:76"/><i><font color="Green">E39</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H</font>) <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H</font>),<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H</font>)</span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H</font>) <a href="funct_4.html#NR1" target="_self">&lt;=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">G</font>) )
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>thus </b><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b</font> = 
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">H</font>) <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="domain_1.html#K1">]</a></span>

<br/>.= 
<font color="Maroon">a'</font> <a href="group_1.html#K1">*</a> <font color="Maroon">b'</font>
<b>by </b><i><a class="ref" href="monoid_0.html#T1" target="_self">Th1</a>, <a class="txt" href="monoid_0.html#E2:76"><i><font color="Green">E39</font></i></a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>
;<br/>


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