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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="group_3.html#V1">normal</a>  <a href="group_2.html#M1">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="group_2.html#K7">carr</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="group_6.html#K6" target="_self">./.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="group_6.html#T27" target="_self">Th27</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="group_6.html#K6" target="_self">./.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:31_1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="group_2.html#K12">*</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="group_2.html#K13">*</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="group_6.html#T15" target="_self">Th15</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="group_6.html#K7" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_6.html#K7" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_6.html#T24" target="_self">Th24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="group_2.html#K12">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_2.html#K10">*</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="group_6.html#E2:31_1"><i><font color="Green">E26</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="group_2.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K7">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_4.html#T60">GROUP_4:60</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="group_2.html#K3">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_4.html#T58">GROUP_4:58</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="group_6.html#E2:31_1"><i><font color="Green">E26</font></i></a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="group_1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> = 
<span class="p1">(<span class="default"><a href="group_6.html#K7" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="group_2.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_6.html#K7" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_6.html#T24" target="_self">Th24</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="group_2.html#K11">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_2.html#K13">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="group_6.html#E2:31_1"><i><font color="Green">E26</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="group_4.html#K7">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_2.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="group_4.html#T61">GROUP_4:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_2.html#K7">carr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="group_2.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="group_4.html#T58">GROUP_4:58</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="group_6.html#E2:31_1"><i><font color="Green">E26</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:31"/>
 <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="group_6.html#K6" target="_self">./.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_2.html#K7">carr</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="group_1.html#T10">GROUP_1:10</a></i>;<br/>


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