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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> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>  st ( for <font color="Olive" title="b2">H</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>  holds not <font color="Olive" title="b2">H</font> is <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a> ) holds <br/><font color="Olive" title="b1">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c1">G</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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">H</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>  holds not <font color="Olive" title="b1">H</font> is <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</a> ) implies <font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c1">G</font> )</span><br/>



<b>assume </b><a NAME="E1:49"/>
for <font color="Olive" title="b1">H</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>  holds not <font color="Olive" title="b1">H</font> is <a href="group_4.html#V2" title="GROUP_4:attr.2">maximal</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="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c1">G</font></span><br/>

<a NAME="E2:49"/><b>then </b>
 <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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="c1">G</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">G</font> #)
 
<b>by </b><i><a class="ref" href="group_4.html#D8" target="_self" title="GROUP_4:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E3:49"/>
<font color="Maroon" title="c2">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_4.html#K6" title="GROUP_4:func.6">Phi</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</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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