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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">H</font> being <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>  st  <a href="group_2.html#K17" title="GROUP_2:func.17">index</a> <font color="Olive" title="b1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Maroon" title="c1">G</font> holds <br/><font color="Olive" title="b1">H</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a>  <a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font></span><br/><b>let </b><font color="Maroon" title="c2">H</font> be  <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="group_2.html#K17" title="GROUP_2:func.17">index</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Maroon" title="c1">G</font> implies <font color="Maroon" title="c2">H</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a>  <a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font> )</span><br/>



<b>assume </b><a NAME="E1:151"/>
 <a href="group_2.html#K17" title="GROUP_2:func.17">index</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Maroon" title="c1">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">H</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a>  <a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font></span><br/>

<a NAME="E2:151"/><b>then </b>
( 1 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Maroon" title="c2">H</font></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Maroon" title="c1">G</font></span>)</span> &amp;  <a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="group_2.html#T177" target="_self" title="GROUP_2:th.177">Th177</a>, <a class="ref" href="group_1.html#T90" title="GROUP_1:th.90">GROUP_1:90</a></i>;<br/>
<b>hence </b><a NAME="E3:151"/>
<font color="Maroon" title="c2">H</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a>  <a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="group_2.html#T82" target="_self" title="GROUP_2:th.82">Th82</a>, <a class="ref" href="xcmplx_1.html#T5" title="XCMPLX_1:th.5">XCMPLX_1:5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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