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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">H3</font> being   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">H2</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>  st <font color="Olive" title="b2">H1</font>,<font color="Olive" title="b3">H2</font> <a href="group_3.html#R6" title="GROUP_3:pred.6">are_conjugated</a>  &amp; <font color="Olive" title="b3">H2</font>,<font color="Olive" title="b1">H3</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a>  holds <br/><font color="Olive" title="b2">H1</font>,<font color="Olive" title="b1">H3</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a> </span><br/><b>let </b><font color="Maroon" title="c2">H3</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</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"> for <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">H2</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>  st <font color="Olive" title="b1">H1</font>,<font color="Olive" title="b2">H2</font> <a href="group_3.html#R6" title="GROUP_3:pred.6">are_conjugated</a>  &amp; <font color="Olive" title="b2">H2</font>,<font color="Maroon" title="c2">H3</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a>  holds <br/><font color="Olive" title="b1">H1</font>,<font color="Maroon" title="c2">H3</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a> </span><br/><b>let </b><font color="Maroon" title="c3">H1</font>, <font color="Maroon" title="c4">H2</font> be  <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c4">H2</font> <a href="group_3.html#R6" title="GROUP_3:pred.6">are_conjugated</a>  &amp; <font color="Maroon" title="c4">H2</font>,<font color="Maroon" title="c2">H3</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a>  implies <font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c2">H3</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a>  )</span><br/>





<b>given </b><font color="Maroon" title="c5">g</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><a NAME="E2:111"/><i><font color="Green" title="E74">A1</font></i>: 
 <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">H1</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c3">H1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">H2</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c5">g</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_3.html#D11" target="_self" title="GROUP_3:def.11">GROUP_3:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">H2</font>,<font color="Maroon" title="c2">H3</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a>  or <font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c2">H3</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a>  )</span><br/>

<b>given </b><font color="Maroon" title="c6">h</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><a NAME="E4:111"/><i><font color="Green" title="E75">A2</font></i>: 
 <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">H2</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c4">H2</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H3</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c6">h</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="group_3.html#D11" target="_self" title="GROUP_3:def.11">GROUP_3:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c2">H3</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a> </span><br/>

<a NAME="E5:111"/>
<font color="Maroon" title="c3">H1</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c2">H3</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">g</font></span>)</span>
 
<b>by </b><i><a class="txt" href="group_3.html#E2:111"><i><font color="Green" title="E74">A1</font></i></a>, <a class="txt" href="group_3.html#E4:111"><i><font color="Green" title="E75">A2</font></i></a>, <a class="ref" href="group_3.html#T72" target="_self" title="GROUP_3:th.72">Th72</a></i>;<br/>
<b>hence </b><a NAME="E6:111"/>
<font color="Maroon" title="c3">H1</font>,<font color="Maroon" title="c2">H3</font> <a href="group_3.html#R5" title="GROUP_3:pred.5">are_conjugated</a> 
 <b>by </b><i><a class="ref" href="group_3.html#D11" target="_self" title="GROUP_3:def.11">Def11</a></i>; <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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