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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a> ; <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">E</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">E</font><br/> for <font color="Olive" title="b3">T</font> being  <a href="group_10.html#NM1" title="GROUP_10:NM.1">LeftOperation</a> of <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">E</font>  holds not  <a href="group_10.html#K13" title="GROUP_10:func.13">the_orbit_of</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">T</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">E</font><br/> for <font color="Olive" title="b2">T</font> being  <a href="group_10.html#NM1" title="GROUP_10:NM.1">LeftOperation</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">E</font>  holds not  <a href="group_10.html#K13" title="GROUP_10:func.13">the_orbit_of</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">T</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">E</font>; <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">T</font> being  <a href="group_10.html#NM1" title="GROUP_10:NM.1">LeftOperation</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">E</font>  holds not  <a href="group_10.html#K13" title="GROUP_10:func.13">the_orbit_of</a> <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">T</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">T</font> be   <a href="group_10.html#NM1" title="GROUP_10:NM.1">LeftOperation</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not  <a href="group_10.html#K13" title="GROUP_10:func.13">the_orbit_of</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">T</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/>







<a NAME="E1:29"/>
<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c3">x</font> <a href="group_10.html#R2" title="GROUP_10:pred.2">are_conjugated_under</a> <font color="Maroon" title="c4">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_10.html#T4" target="_self" title="GROUP_10:th.4">Th4</a></span>;<br/>
<a NAME="E2:29"/><span class="kw">then </span>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">E</font> : <font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">y</font> <a href="group_10.html#R2" title="GROUP_10:pred.2">are_conjugated_under</a> <font color="Maroon" title="c4">T</font> </span>}</span> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:29"/>
not  <a href="group_10.html#K13" title="GROUP_10:func.13">the_orbit_of</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">T</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <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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