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<b>let </b><font color="Maroon" title="c1">O</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  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/>



<b>consider </b><font color="Maroon" title="c3">H</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="group_9.html#L1" title="GROUP_9:struct.1">HGrWOpStr</a> of <font color="Maroon" title="c1">O</font><b> such that </b><br/><a NAME="E2:138"/><i><font color="Green" title="E113">A1</font></i>: 
( <font color="Maroon" title="c3">H</font> is <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_9.html#V3" title="GROUP_9:attr.3">distributive</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">Group-like</a> &amp; <font color="Maroon" title="c3">H</font> is <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> &amp; <font color="Maroon" title="c2">G</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="c3">H</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c3">H</font> #) )
 <b>by </b><i><a class="txt" href="group_9.html#E8"><i><font color="Green" title="E8">Lm3</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">H</font> = <font color="Maroon" title="c3">H</font> as  <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a> <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font> <b>by </b><i><a class="txt" href="group_9.html#E2:138"><i><font color="Green" title="E113">A1</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">H</font>
;<br/>

<b>thus </b><a NAME="E4:138"/>
<font color="Maroon" title="c2">G</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="c4">H</font>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c4">H</font> #)
 <b>by </b><i><a class="txt" href="group_9.html#E2:138"><i><font color="Green" title="E113">A1</font></i></a></i>;<br/>


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