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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">H</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>assume </b><a NAME="E1:135"/>
 <a href="group_2.html#K15" title="GROUP_2:func.15">Right_Cosets</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<a NAME="E2:135"/><b>then </b><i><font color="Green" title="E93">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_2.html#K15" title="GROUP_2:func.15">Right_Cosets</a> <font color="Maroon" title="c2">H</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">T</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font> ;<br/>
<b>consider </b><font color="Maroon" title="c4">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E5:135"/><i><font color="Green" title="E94">A2</font></i>: 
<font color="Maroon" title="c3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> <a href="group_2.html#K13" title="GROUP_2:func.13">*</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="txt" href="group_2.html#E2:135"><i><font color="Green" title="E93">A1</font></i></a>, <a class="ref" href="group_2.html#D16" target="_self" title="GROUP_2:def.16">Def16</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="135_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">g</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><a NAME="E1:135_1"/>
 ex <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Maroon" title="c5">g</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">a</font> &amp; <font color="Olive" title="b1">b</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c2">H</font> )
 <b>by </b><i><a class="txt" href="group_2.html#E5:135"><i><font color="Green" title="E94">A2</font></i></a>, <a class="ref" href="group_2.html#T126" target="_self" title="GROUP_2:th.126">Th126</a></i>;<br/><b>hence </b><a NAME="E2:135_1"/>
<font color="Maroon" title="c5">g</font> <a href="rlvect_1.html#R1" title="RLVECT_1:pred.1">in</a> <font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="ref" href="group_1.html#T14" title="GROUP_1:th.14">GROUP_1:14</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:135"/>
<font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="group_2.html#T71" target="_self" title="GROUP_2:th.71">Th71</a></i>;<br/>


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