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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/>

<b>assume </b><a NAME="E1:61_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D3">GROUP_1:def 3</a>
<div class="add"><b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>take </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><a NAME="E2:61_1_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="topgrp_1.html#E1:61_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/><b>take </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font>;<br/><b>thus </b><a NAME="E3:61_1_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="topgrp_1.html#E1:61_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E3:61_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="topgrp_1.html#E1:61_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a><br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D16">GROUP_1:def 16</a><br/>

<b>thus </b><a NAME="E4:61_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="topgrp_1.html#E1:61_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/>


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