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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c4">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:1"/><i><font color="Green" title="E1">A1</font></i>: 
 <a href="group_1.html#K7" title="GROUP_1:func.7">ord</a> <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>and </b><br/><a NAME="E2:1"/><i><font color="Green" title="E2">A2</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> <font color="Maroon" title="c4">k</font>
 <b>and </b><br/><a NAME="E3:1"/><i><font color="Green" title="E3">A3</font></i>: 
<font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ;<br/>

<a NAME="E4:1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="txt" href="gr_cy_2.html#E2:1"><i><font color="Green" title="E2">A2</font></i></a>, <a class="txt" href="gr_cy_2.html#E3:1"><i><font color="Green" title="E3">A3</font></i></a>, <a class="ref" href="group_1.html#T43" title="GROUP_1:th.43">GROUP_1:43</a></i>;<br/>
<b>hence </b><a NAME="E5:1"/>
contradiction
 <b>by </b><i><a class="txt" href="gr_cy_2.html#E1:1"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="group_1.html#T84" title="GROUP_1:th.84">GROUP_1:84</a></i>;<br/>


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