<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">T1</font>, <font color="Maroon" title="c5">T2</font> be   <a href="group_10.html#NM1" title="GROUP_10:NM.1">LeftOperation</a> of <font color="Maroon" title="c3">H</font>,<span class="p1">(<span class="default"><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>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">h</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">H</font> holds  <font color="Maroon" title="c4">T1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_10.html#K16" title="GROUP_10:func.16">the_left_translation_of</a> <font color="Olive" title="b1">h</font>,<font color="Maroon" title="c2">p</font> ) &amp; ( for <font color="Olive" title="b1">h</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">H</font> holds  <font color="Maroon" title="c5">T2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_10.html#K16" title="GROUP_10:func.16">the_left_translation_of</a> <font color="Olive" title="b1">h</font>,<font color="Maroon" title="c2">p</font> ) implies <font color="Maroon" title="c4">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">T2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:52_1_2"/><span class="lab"><font color="Green" title="E38">A26</font></span>: 
for <font color="Olive" title="b1">h</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">H</font> holds  <font color="Maroon" title="c4">T1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_10.html#K16" title="GROUP_10:func.16">the_left_translation_of</a> <font color="Olive" title="b1">h</font>,<font color="Maroon" title="c2">p</font>
 <span class="kw">and </span><br/><a NAME="E2:52_1_2"/><span class="lab"><font color="Green" title="E39">A27</font></span>: 
for <font color="Olive" title="b1">h</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">H</font> holds  <font color="Maroon" title="c5">T2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_10.html#K16" title="GROUP_10:func.16">the_left_translation_of</a> <font color="Olive" title="b1">h</font>,<font color="Maroon" title="c2">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">T1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">T2</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">H</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="funct_2.html#D9" title="FUNCT_2:def.9">FUNCT_2:def 9</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="group_10.html#NK1" title="GROUP_10:NK.1">^</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_10.html#NK1" title="GROUP_10:NK.1">^</a> </span><br/>

<span class="kw">thus </span><font color="Maroon" title="c4">T1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font> = 
 <a href="group_10.html#K16" title="GROUP_10:func.16">the_left_translation_of</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c2">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_2"><span class="lab"><font color="Green" title="E38">A26</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c5">T2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_1_2"><span class="lab"><font color="Green" title="E39">A27</font></span></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/>


</div>
