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<b>let </b><font color="Maroon">G</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/>



<b>thus </b><a NAME="E1:84"/>
( <font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_5.html#K10" target="_self">center</a> <font color="Maroon">G</font> implies for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> holds  <font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:84_1"/>
<font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_5.html#K10" target="_self">center</a> <font color="Maroon">G</font>
 ;<br/>

<a NAME="E2:84_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" target="_self">center</a> <font color="Maroon">G</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E3:84_1"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b</font> where <font color="Olive">b</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> : for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> holds  <font color="Olive">b</font> <a href="group_1.html#K1">*</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> </span>}</span> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:84_1"/><b>then </b>
 ex <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> st <br/>( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> &amp; ( for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> holds  <font color="Olive">b</font> <a href="group_1.html#K1">*</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> ) )
 
;<br/>
<b>hence </b><a NAME="E5:84_1"/>
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> holds  <font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font>
 ;<br/>


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

<b>assume </b><a NAME="E2:84"/>
for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> holds  <font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font>
 ;<br/>

<a NAME="E3:84"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">c</font> where <font color="Olive">c</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> : for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font> holds  <font color="Olive">c</font> <a href="group_1.html#K1">*</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="group_1.html#K1">*</a> <font color="Olive">c</font> </span>}</span> 
 
;<br/>
<a NAME="E4:84"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_5.html#K10" target="_self">center</a> <font color="Maroon">G</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:84"/>
<font color="Maroon">a</font> <a href="rlvect_1.html#R1">in</a>  <a href="group_5.html#K10" target="_self">center</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>


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