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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G3</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="group_1.html#V3" title="GROUP_1:attr.3">Group-like</a>  <a href="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a> ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">A</font> = <span class="p1"><a href="group_7.html#K18" title="GROUP_7:func.18">&lt;*</a><span class="default"><font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</font></span><a href="group_7.html#K18" title="GROUP_7:func.18">*&gt;</a></span> as   <a href="group_7.html#NM1" title="GROUP_7:NM.1">HGrStr-Family</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> ;<br/>
<a NAME="E2:60"/>
<font color="Maroon" title="c4">A</font> is <a href="group_7.html#V2" title="GROUP_7:attr.2">Group-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_7.html#D6" target="_self" title="GROUP_7:def.6">GROUP_7:def 6</a><br/>

<a NAME="E1:60_1"/>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 
<b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E2:60_1"/>
<font color="Maroon" title="c4">A</font> <a href="group_7.html#K1" title="GROUP_7:func.1">.</a> <font color="Maroon" title="c5">x</font> is <a href="group_1.html#V3" title="GROUP_1:attr.3">Group-like</a>
 <b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:60"/>
<span class="p1"><a href="group_7.html#K18" title="GROUP_7:func.18">&lt;*</a><span class="default"><font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</font></span><a href="group_7.html#K18" title="GROUP_7:func.18">*&gt;</a></span> is  <a href="group_7.html#V2" title="GROUP_7:attr.2">Group-like</a> <a href="group_7.html#NM1" title="GROUP_7:NM.1">HGrStr-Family</a> of <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 ;<br/>


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