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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font> holds <br/> ( <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K8" title="GROUP_3:func.8">con_class</a> <font color="Olive" title="b2">B</font> iff <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a>  )</span><br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K8" title="GROUP_3:func.8">con_class</a> <font color="Maroon" title="c3">B</font> iff <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a>  )</span><br/>





<b>thus </b><a NAME="E1:99"/>
( <font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K8" title="GROUP_3:func.8">con_class</a> <font color="Maroon" title="c3">B</font> implies <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a>  )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a>  implies <font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K8" title="GROUP_3:func.8">con_class</a> <font color="Maroon" title="c3">B</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="99_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:99_1"/>
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K8" title="GROUP_3:func.8">con_class</a> <font color="Maroon" title="c3">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a> </span><br/>

<a NAME="E2:99_1"/><b>then </b>
 ex <font color="Olive" title="b1">C</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">C</font> &amp; <font color="Maroon" title="c3">B</font>,<font color="Olive" title="b1">C</font> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a>  )
 
;<br/>
<b>hence </b><a NAME="E3:99_1"/>
<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:99"/>
<font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> <a href="group_3.html#R4" title="GROUP_3:pred.4">are_conjugated</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K8" title="GROUP_3:func.8">con_class</a> <font color="Maroon" title="c3">B</font></span><br/>

<b>hence </b><a NAME="E3:99"/>
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="group_3.html#K8" title="GROUP_3:func.8">con_class</a> <font color="Maroon" title="c3">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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