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<span class="kw">let </span><font color="Maroon" title="c1">p</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G</font> being   <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>  st  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> holds <br/><font color="Olive" title="b1">G</font> is <font color="Maroon" title="c1">p</font> <a href="groupp_1.html#V3" title="GROUPP_1:attr.3">-commutative-group</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> implies <font color="Maroon" title="c2">G</font> is <font color="Maroon" title="c1">p</font> <a href="groupp_1.html#V3" title="GROUPP_1:attr.3">-commutative-group</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:47"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
 <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">G</font> is <font color="Maroon" title="c1">p</font> <a href="groupp_1.html#V3" title="GROUPP_1:attr.3">-commutative-group</a> </span><br/>

<a NAME="E2:47"/>
<font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T5" title="NEWTON:th.5">NEWTON:5</a></span>;<br/>
<a NAME="E3:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A2</font></span>: 
<font color="Maroon" title="c2">G</font> is <font color="Maroon" title="c1">p</font> <a href="group_10.html#V2" title="GROUP_10:attr.2">-group</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="group_10.html#D17" title="GROUP_10:def.17">GROUP_10:def 17</a></span>;<br/>
<a NAME="E4:47"/>
<font color="Maroon" title="c2">G</font> is   <a href="gr_cy_1.html#V1" title="GR_CY_1:attr.1">cyclic</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="gr_cy_1.html#T21" title="GR_CY_1:th.21">GR_CY_1:21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:47"/>
<font color="Maroon" title="c2">G</font> is <font color="Maroon" title="c1">p</font> <a href="groupp_1.html#V3" title="GROUPP_1:attr.3">-commutative-group</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47"><span class="lab"><font color="Green" title="E27">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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