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<b>reconsider </b><font color="Maroon" title="c4">H'</font> =  <a href="group_9.html#K4" title="GROUP_9:func.4">(1).</a> <font color="Maroon" title="c3">H</font> as   <a href="group_9.html#NM2" title="GROUP_9:NM.2">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">H'</font> = <font color="Maroon" title="c4">H'</font> as    <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c3">H</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c5">H'</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">H'</font> is <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">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="c3">H</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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="c5">H'</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c5">H'</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">H''</font> implies <font color="Maroon" title="c6">H''</font> is <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a> )</span><br/><b>assume </b><a NAME="E1:23_1_1_1"/><i><font color="Green" title="E15">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="c5">H'</font>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c5">H'</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">H''</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">H''</font> is <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a></span><br/><b>reconsider </b><font color="Maroon" title="c7">H</font> = <font color="Maroon" title="c3">H</font> as   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> ;<br/><a NAME="E3:23_1_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">H''</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c7">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="#E1:23_1_1_1"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="group_9.html#D8" target="_self" title="GROUP_9:def.8">Def8</a></i>;<br/><a NAME="E4:23_1_1_1"/><b>then </b>
<font color="Maroon" title="c6">H''</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c7">H</font>
 <b>by </b><i><a class="ref" href="group_2.html#D7" title="GROUP_2:def.7">GROUP_2:def 7</a></i>;<br/><b>hence </b><a NAME="E5:23_1_1_1"/>
<font color="Maroon" title="c6">H''</font> is <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</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>hence </b><a NAME="E4:23_1_1"/>
<font color="Maroon" title="c5">H'</font> is <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>
 <b>by </b><i><a class="ref" href="group_9.html#D10" target="_self" title="GROUP_9:def.10">Def10</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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