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<span class="kw">consider </span><font color="Maroon" title="c3">P</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><span class="kw"> such that </span><br/><a NAME="E2:50_1_1"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="group_10.html#R5" title="GROUP_10:pred.5">is_Sylow_p-subgroup_of_prime</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_10.html#T12" target="_self" title="GROUP_10:th.12">Th12</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">P9</font> =  <a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c3">P</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">H9</font> =  <a href="group_2.html#K7" title="GROUP_2:func.7">(Omega).</a> <font color="Maroon" title="c3">P</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="group_3.html#K1" title="GROUP_3:func.1">Subgroups</a> <font color="Maroon" title="c1">G</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#D1" title="GROUP_3:def.1">GROUP_3:def 1</a></span>;<br/>
<a NAME="E4:50_1_1"/>
<font color="Maroon" title="c5">H9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_10.html#K15" title="GROUP_10:func.15">the_sylow_p-subgroups_of_prime</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50_1_1"><span class="lab"><font color="Green" title="E37">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:50_1_1"/>
( not  <a href="group_10.html#K15" title="GROUP_10:func.15">the_sylow_p-subgroups_of_prime</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">G</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <a href="group_10.html#K15" title="GROUP_10:func.15">the_sylow_p-subgroups_of_prime</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">G</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finset_1.html#T13" title="FINSET_1:th.13">FINSET_1:13</a>, <a class="ref" href="group_3.html#T19" title="GROUP_3:th.19">GROUP_3:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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