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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">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds   <a href="group_1.html#K6" title="GROUP_1:func.6">ord</a> <font color="Olive" title="b1">a</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c1">G</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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_1.html#K6" title="GROUP_1:func.6">ord</a> <font color="Maroon" title="c2">a</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c1">G</font></span><br/>



<a NAME="E1:12"/>
 <a href="group_1.html#K6" title="GROUP_1:func.6">ord</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <span class="p1">(<span class="default"><a href="group_4.html#K5" title="GROUP_4:func.5">gr</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="gr_cy_1.html#T27" target="_self" title="GR_CY_1:th.27">Th27</a></i>;<br/>
<b>hence </b><a NAME="E2:12"/>
 <a href="group_1.html#K6" title="GROUP_1:func.6">ord</a> <font color="Maroon" title="c2">a</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="group_2.html#T178" title="GROUP_2:th.178">GROUP_2:178</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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