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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">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>assume </b><a NAME="E1:9"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c2">b</font> <a href="group_1.html#NR2" title="GROUP_1:NR.2">is_of_order_0</a> 
 ;<br/>

<a NAME="E2:9"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> <font color="Olive" title="b1">n</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> holds <br/><font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:9_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> </span>)</span> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> <font color="Maroon" title="c3">n</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>
 ;<br/>

<a NAME="E2:9_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  <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="ref" href="group_1.html#T51" title="GROUP_1:th.51">GROUP_1:51</a></i>;<br/>
<a NAME="E3:9_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a> 
 
<b>by </b><i><a class="ref" href="group_1.html#T16" title="GROUP_1:th.16">GROUP_1:16</a></i>;<br/>
<a NAME="E4:9_1"/><b>then </b>
<font color="Maroon" title="c2">b</font> <a href="group_1.html#K6" title="GROUP_1:func.6">|^</a> <font color="Maroon" title="c3">n</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="ref" href="group_1.html#T17" title="GROUP_1:th.17">GROUP_1:17</a></i>;<br/>
<b>hence </b><a NAME="E5:9_1"/>
<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="group_8.html#E1:9"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="group_1.html#D11" title="GROUP_1:def.11">GROUP_1:def 11</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:9"/>
<font color="Maroon" title="c2">b</font> <a href="group_1.html#K3" title="GROUP_1:func.3">"</a>  <a href="group_1.html#NR2" title="GROUP_1:NR.2">is_of_order_0</a> 
 <b>by </b><i><a class="ref" href="group_1.html#D11" title="GROUP_1:def.11">GROUP_1:def 11</a></i>;<br/>


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