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<b>let </b><font color="Maroon" title="c1">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="c2">M</font> be    <a href="monoid_0.html#M1" title="MONOID_0:mode.1">MonoidalExtension</a> of <font color="Maroon" title="c1">G</font>;<br/>



<a NAME="E1:46"/><i><font color="Green" title="E29">A1</font></i>: 
 <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">M</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">M</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c1">G</font> #)
 
<b>by </b><i><a class="ref" href="monoid_0.html#D22" target="_self" title="MONOID_0:def.22">Def22</a></i>;<br/>
<b>hence </b><a NAME="E2:46"/>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">M</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">G</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">M</font>) <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">G</font>) )
 ;<br/>

<b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">M</font>;<br/><b>let </b><font color="Maroon" title="c5">a'</font>, <font color="Maroon" title="c6">b'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>thus </b><a NAME="E3:46"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a'</font> &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b'</font> implies <font color="Maroon" title="c3">a</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a'</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c6">b'</font> )
 <b>by </b><i><a class="txt" href="monoid_0.html#E1:46"><i><font color="Green" title="E29">A1</font></i></a></i>;<br/>


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