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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:16_2_1_1"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="group_7.html#V3" target="_self">associative</a>
 ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><a NAME="E2:16_2_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being 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>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="group_7.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="group_7.html#E1:16_2_1_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="group_7.html#D4" target="_self">Def4</a></i>;<br/><b>hence </b><a NAME="E3:16_2_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_7.html#K1" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> is <a href="group_1.html#V4">associative</a>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:16_2_1"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="group_7.html#K1" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> is <a href="group_1.html#V4">associative</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_7.html#D4" target="_self">GROUP_7:def 4</a><br/>

<b>assume </b><a NAME="E3:16_2_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="group_7.html#K1" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font> as  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>  <b>by </b><i><a class="txt" href="group_7.html#E2:16_2_1"><i><font color="Green">E9</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E6:16_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


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