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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>thus </b><a NAME="E1:98"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="group_2.html#K12" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font> implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> st <br/>( <font color="Maroon">c<sub>1</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="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>4</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:98_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="group_2.html#K12" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:98_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="group_2.html#K3" target="_self">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
;<br/>
<b>then 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>2</sub></font><b> such that </b><br/><a NAME="E4:98_1"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>1</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>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="group_2.html#T33" target="_self">Th33</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E5:98_1"/>
( <font color="Maroon">c<sub>1</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>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="group_2.html#E4:98_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="group_2.html#T88" target="_self">Th88</a></i>;<br/>


</div><b>end;</b></div>

<b>given </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><a NAME="E2:98"/><i><font color="Green">E65</font></i>: 
( <font color="Maroon">c<sub>1</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>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<a NAME="E3:98"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="group_2.html#E2:98"><i><font color="Green">E65</font></i></a>, <a class="ref" href="group_2.html#T88" target="_self">Th88</a></i>;<br/>
<a NAME="E4:98"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="group_2.html#K3" target="_self">*</a> <span class="p1">(<span class="default"><a href="group_2.html#K7" target="_self">carr</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="group_2.html#E2:98"><i><font color="Green">E65</font></i></a>, <a class="ref" href="group_2.html#T33" target="_self">Th33</a></i>;<br/>
<b>hence </b><a NAME="E5:98"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="group_2.html#K12" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>


</div>
