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<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">H</font> be  <a href="group_1.html#V1" title="GROUP_1:attr.1">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>;<br/>



<b>thus </b><a NAME="E1:149"/>
( <font color="Maroon" title="c2">H</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> implies  <a href="group_3.html#K11" title="GROUP_3:func.11">Normalizator</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="149_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:149_1"/><i><font color="Green" title="E95">A1</font></i>: 
<font color="Maroon" title="c2">H</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="149_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><a NAME="E1:149_1_1"/>
<font color="Maroon" title="c2">H</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c3">a</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="txt" href="group_3.html#E1:149_1"><i><font color="Green" title="E95">A1</font></i></a>, <a class="ref" href="group_3.html#D13" target="_self" title="GROUP_3:def.13">Def13</a></i>;<br/><b>hence </b><a NAME="E2:149_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_3.html#K11" title="GROUP_3:func.11">Normalizator</a> <font color="Maroon" title="c2">H</font>
 <b>by </b><i><a class="ref" href="group_3.html#T160" target="_self" title="GROUP_3:th.160">Th160</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:149_1"/>
 <a href="group_3.html#K11" title="GROUP_3:func.11">Normalizator</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="group_2.html#T71" title="GROUP_2:th.71">GROUP_2:71</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:149"/><i><font color="Green" title="E95">A2</font></i>: 
 <a href="group_3.html#K11" title="GROUP_3:func.11">Normalizator</a> <font color="Maroon" title="c2">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font>
 ;<br/>

<a NAME="E3:149"/>
<font color="Maroon" title="c2">H</font> is <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="149_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_3.html#D13" target="_self" title="GROUP_3:def.13">GROUP_3:def 13</a><br/>

<a NAME="E1:149_2"/>
<font color="Maroon" title="c3">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="group_3.html#K11" title="GROUP_3:func.11">Normalizator</a> <font color="Maroon" title="c2">H</font>
 
<b>by </b><i><a class="txt" href="group_3.html#E2:149"><i><font color="Green" title="E95">A2</font></i></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></i>;<br/>
<a NAME="E2:149_2"/><b>then </b>
 ex <font color="Olive" title="b1">b</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c2">H</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Olive" title="b1">b</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Maroon" title="c2">H</font> )
 
<b>by </b><i><a class="ref" href="group_3.html#T160" target="_self" title="GROUP_3:th.160">Th160</a></i>;<br/>
<b>hence </b><a NAME="E3:149_2"/>
<font color="Maroon" title="c2">H</font> <a href="group_3.html#K6" title="GROUP_3:func.6">|^</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#G1" title="GROUP_1:aggr.1">HGrStr</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="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">H</font> #)
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:149"/>
<font color="Maroon" title="c2">H</font> is  <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>
 ;<br/>


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