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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_1.html#V1">strict</a>  <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:148"/><i><font color="Green">E97</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="group_1.html#V6">finite</a> &amp;  <a href="group_2.html#K17" target="_self">index</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K9">ord</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:148"/><b>then </b>
( 1 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K9">ord</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K9">ord</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K9">ord</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp;  <a href="group_1.html#K9">ord</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 
<b>by </b><i><a class="ref" href="group_2.html#T177" target="_self">Th177</a>, <a class="ref" href="group_1.html#T90">GROUP_1:90</a></i>;<br/>
<a NAME="E3:148"/><b>then </b>
(  <a href="group_1.html#K9">ord</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="group_1.html#V6">finite</a> )
 
<b>by </b><i><a class="txt" href="group_2.html#E1:148"><i><font color="Green">E97</font></i></a>, <a class="ref" href="group_2.html#T48" target="_self">Th48</a>, <a class="ref" href="xcmplx_1.html#T5">XCMPLX_1:5</a></i>;<br/>
<b>hence </b><a NAME="E4:148"/>
<font color="Maroon">c<sub>2</sub></font> <a href="group_2.html#R1" target="_self">=</a>  <a href="group_2.html#K5" target="_self">(1).</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="group_2.html#T82" target="_self">Th82</a></i>;<br/>


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