<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">G1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V4">associative</a>  <a href="group_1.html#L1">HGrStr</a> , <font color="Maroon">G2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V4">associative</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/>

<b>reconsider </b><font color="Maroon">A</font> = <span class="p1"><a href="group_7.html#K11" target="_self">&lt;*</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font></span><a href="group_7.html#K11" target="_self">*&gt;</a></span> as   <a href="group_7.html#NM1">HGrStr-Family</a> of <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span> ;<br/>
<a NAME="E2:50"/>
<font color="Maroon">A</font> is <a href="group_7.html#V3" target="_self">associative</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_7.html#D7" target="_self">GROUP_7:def 7</a><br/>

<a NAME="E1:50_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 2 )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:50_1"/>
<font color="Maroon">A</font> <a href="group_7.html#K1" target="_self">.</a> <font color="Maroon">x</font> is <a href="group_1.html#V4">associative</a>
 <b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:50"/>
<span class="p1"><a href="group_7.html#K11" target="_self">&lt;*</a><span class="default"><font color="Maroon">G1</font>,<font color="Maroon">G2</font></span><a href="group_7.html#K11" target="_self">*&gt;</a></span> is  <a href="group_7.html#V3" target="_self">associative</a> <a href="group_7.html#NM1">HGrStr-Family</a> of <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 ;<br/>


</div>
