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<b>let </b><font color="Maroon" title="c1">G1</font> be  <a href="group_1.html#V6" title="GROUP_1:attr.6">commutative</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/>

<b>reconsider </b><font color="Maroon" title="c2">A</font> = <span class="p1"><a href="group_7.html#K8" title="GROUP_7:func.8">&lt;*</a><span class="default"><font color="Maroon" title="c1">G1</font></span><a href="group_7.html#K8" title="GROUP_7:func.8">*&gt;</a></span> as   <a href="group_7.html#NM1" title="GROUP_7:NM.1">HGrStr-Family</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ;<br/>
<a NAME="E2:38"/>
<font color="Maroon" title="c2">A</font> is <a href="group_7.html#V4" title="GROUP_7:attr.4">commutative</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_7.html#D8" target="_self" title="GROUP_7:def.8">GROUP_7:def 8</a><br/>

<a NAME="E1:38_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E2:38_1"/>
<font color="Maroon" title="c2">A</font> <a href="group_7.html#K1" title="GROUP_7:func.1">.</a> <font color="Maroon" title="c3">x</font> is <a href="group_1.html#V6" title="GROUP_1:attr.6">commutative</a>
 <b>by </b><i><a class="ref" href="finseq_1.html#D8" title="FINSEQ_1:def.8">FINSEQ_1:def 8</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:38"/>
<span class="p1"><a href="group_7.html#K8" title="GROUP_7:func.8">&lt;*</a><span class="default"><font color="Maroon" title="c1">G1</font></span><a href="group_7.html#K8" title="GROUP_7:func.8">*&gt;</a></span> is  <a href="group_7.html#V2" title="GROUP_7:attr.2">Group-like</a> <a href="group_7.html#V3" title="GROUP_7:attr.3">associative</a> <a href="group_7.html#V4" title="GROUP_7:attr.4">commutative</a> <a href="group_7.html#NM1" title="GROUP_7:NM.1">HGrStr-Family</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>


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