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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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>  st <font color="Maroon" title="c1">G</font> is   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> holds <br/><font color="Olive" title="b1">H</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">H</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> implies <font color="Maroon" title="c2">H</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:122"/>
<font color="Maroon" title="c1">G</font> is   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">H</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:122"/>
 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> holds  <font color="Maroon" title="c2">H</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Olive" title="b1">a</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="c2">H</font>, the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c2">H</font> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="group_3.html#T73" target="_self" title="GROUP_3:th.73">Th86</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_3.html#D13" target="_self" title="GROUP_3:def.13">GROUP_3:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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