<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">O</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">G</font> being   <a href="group_9.html#NM1" title="GROUP_9:NM.1">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font><br/>  for <font color="Olive" title="b2">N</font> being   <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>   <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Olive" title="b1">G</font> holds   <a href="group_9.html#K13" title="GROUP_9:func.13">Ker</a> <span class="p1">(<span class="default"><a href="group_9.html#K12" title="GROUP_9:func.12">nat_hom</a> <font color="Olive" title="b2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">N</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="group_9.html#NM1" title="GROUP_9:NM.1">GroupWithOperators</a> of <font color="Maroon" title="c1">O</font>; <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">N</font> being   <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>   <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font> holds   <a href="group_9.html#K13" title="GROUP_9:func.13">Ker</a> <span class="p1">(<span class="default"><a href="group_9.html#K12" title="GROUP_9:func.12">nat_hom</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">N</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">N</font> be   <a href="group_9.html#V2" title="GROUP_9:attr.2">strict</a>   <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>   <a href="group_9.html#M1" title="GROUP_9:mode.1">StableSubgroup</a> of <font color="Maroon" title="c2">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="group_9.html#K13" title="GROUP_9:func.13">Ker</a> <span class="p1">(<span class="default"><a href="group_9.html#K12" title="GROUP_9:func.12">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">N</font></span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">N9</font> =  <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">N</font>, the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c3">N</font> #) as   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <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="c2">G</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="group_9.html#E20"><span class="lab"><font color="Green" title="E19">Lm7</font></span></a></span>;<br/>
<a NAME="E2:120"/><span class="lab"><font color="Green" title="E98">A1</font></span>: 
(  <a href="group_9.html#K12" title="GROUP_9:func.12">nat_hom</a> <font color="Maroon" title="c3">N</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="group_6.html#K9" title="GROUP_6:func.9">nat_hom</a> <font color="Maroon" title="c4">N9</font> &amp;  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="group_9.html#K10" title="GROUP_9:func.10">./.</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c4">N9</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#D20" target="_self" title="GROUP_9:def.20">Def23</a>, <a class="txt" href="group_9.html#E104"><span class="lab"><font color="Green" title="E93">Lm35</font></span></a></span>;<br/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_9.html#K13" title="GROUP_9:func.13">Ker</a> <span class="p2">(<span class="default"><a href="group_9.html#K12" title="GROUP_9:func.12">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span></span>)</span> = 
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> : <span class="p1">(<span class="default"><a href="group_9.html#K12" title="GROUP_9:func.12">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="group_9.html#K10" title="GROUP_9:func.10">./.</a> <font color="Maroon" title="c3">N</font></span>)</span> </span> } </span> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_9.html#D21" target="_self" title="GROUP_9:def.21">Def24</a></span>
<br/>.= 
<span class="p1"> { <span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">G</font> : <span class="p1">(<span class="default"><a href="group_6.html#K9" title="GROUP_6:func.9">nat_hom</a> <font color="Maroon" title="c4">N9</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">G</font> <a href="group_6.html#K5" title="GROUP_6:func.5">./.</a> <font color="Maroon" title="c4">N9</font></span>)</span> </span> } </span> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:120"><span class="lab"><font color="Green" title="E98">A1</font></span></a></span>
<br/>.= 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_6.html#K10" title="GROUP_6:func.10">Ker</a> <span class="p2">(<span class="default"><a href="group_6.html#K9" title="GROUP_6:func.9">nat_hom</a> <font color="Maroon" title="c4">N9</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#D9" title="GROUP_6:def.9">GROUP_6:def 9</a></span>
<br/>.= 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">N</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_6.html#T43" title="GROUP_6:th.43">GROUP_6:43</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:120"/>
 <a href="group_9.html#K13" title="GROUP_9:func.13">Ker</a> <span class="p1">(<span class="default"><a href="group_9.html#K12" title="GROUP_9:func.12">nat_hom</a> <font color="Maroon" title="c3">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="group_9.html#E12"><span class="lab"><font color="Green" title="E12">Lm5</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
