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

<b>let </b><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</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">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span> holds <br/> (  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> &amp; ( for <font color="Olive" title="b2">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> holds <br/><span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> ) &amp; ( for <font color="Olive" title="b2">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font> holds <br/><font color="Olive" title="b2">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font> ) )</span><br/>

<b>set </b><font color="Maroon" title="c2">C</font> =  <a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font>;<br/>
<b>set </b><font color="Maroon" title="c3">V</font> =  <a href="grcat_1.html#K18" title="GRCAT_1:func.18">GroupObjects</a> <font color="Maroon" title="c1">UN</font>;<br/>
<b>set </b><font color="Maroon" title="c4">X</font> =  <a href="grcat_1.html#K19" title="GRCAT_1:func.19">Morphs</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K18" title="GRCAT_1:func.18">GroupObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span>;<br/>
<b>let </b><font color="Maroon" title="c5">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> &amp; ( for <font color="Olive" title="b1">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> holds <br/><span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> ) &amp; ( for <font color="Olive" title="b1">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> holds <br/><font color="Olive" title="b1">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> ) )</span><br/>

<b>reconsider </b><font color="Maroon" title="c6">b'</font> = <font color="Maroon" title="c5">b</font> as    <a href="grcat_1.html#M2" title="GRCAT_1:mode.2">Element</a> of  <a href="grcat_1.html#K18" title="GRCAT_1:func.18">GroupObjects</a> <font color="Maroon" title="c1">UN</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c7">b''</font> = <font color="Maroon" title="c6">b'</font> as   <a href="algstr_1.html#NM2" title="ALGSTR_1:NM.2">AddGroup</a> ;<br/>
<a NAME="E3:97"/><i><font color="Green" title="E57">A1</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K22" title="GRCAT_1:func.22">ID</a> <font color="Maroon" title="c6">b'</font>
 
<b>by </b><i><a class="ref" href="grcat_1.html#T48" target="_self" title="GRCAT_1:th.48">Th48</a></i>;<br/>
<b>hence </b><i><font color="Green" title="E58">A2</font></i>:  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> = 
 <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K12" title="GRCAT_1:func.12">ID</a> <font color="Maroon" title="c7">b''</font></span>)</span>
<b>by </b><i><a class="ref" href="grcat_1.html#T49" target="_self" title="GRCAT_1:th.49">Th49</a></i>
<br/>.= 
<font color="Maroon" title="c5">b</font>

;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> &amp; ( for <font color="Olive" title="b1">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> holds <br/><span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> ) &amp; ( for <font color="Olive" title="b1">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> holds <br/><font color="Olive" title="b1">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> ) )</span><br/>

<b>thus </b><i><font color="Green" title="E59">A3</font></i>:  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> = 
 <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K12" title="GRCAT_1:func.12">ID</a> <font color="Maroon" title="c7">b''</font></span>)</span>
<b>by </b><i><a class="txt" href="grcat_1.html#E3:97"><i><font color="Green" title="E57">A1</font></i></a>, <a class="ref" href="grcat_1.html#T49" target="_self" title="GRCAT_1:th.49">Th49</a></i>
<br/>.= 
<font color="Maroon" title="c5">b</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">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> holds <br/><span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> ) &amp; ( for <font color="Olive" title="b1">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> holds <br/><font color="Olive" title="b1">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> ) )</span><br/>

<b>thus </b><a NAME="E6:97"/>
for <font color="Olive" title="b1">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> holds <br/><span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</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">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> holds <br/><font color="Olive" title="b1">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> implies <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font> )</span><br/>

<b>assume </b><a NAME="E1:97_3"/><i><font color="Green" title="E60">A4</font></i>: 
 <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c9">f1</font> = <font color="Maroon" title="c8">f</font> as  <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>  <a href="grcat_1.html#M3" title="GRCAT_1:mode.3">Element</a> of  <a href="grcat_1.html#K19" title="GRCAT_1:func.19">Morphs</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K18" title="GRCAT_1:func.18">GroupObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span> <b>by </b><i><a class="ref" href="grcat_1.html#T47" target="_self" title="GRCAT_1:th.47">Th47</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">f'</font> = <font color="Maroon" title="c9">f1</font> as  <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a> <a href="grcat_1.html#NM1" title="GRCAT_1:NM.1">GroupMorphism</a> ;<br/>
<a NAME="E4:97_3"/><i><font color="Green" title="E61">A5</font></i>: 
 <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c10">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b''</font>
 
<b>by </b><i><a class="txt" href="grcat_1.html#E1:97_3"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="grcat_1.html#T49" target="_self" title="GRCAT_1:th.49">Th49</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c8">f</font> = 
<span class="p1">(<span class="default"><a href="grcat_1.html#K12" title="GRCAT_1:func.12">ID</a> <font color="Maroon" title="c7">b''</font></span>)</span> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c10">f'</font>
<b>by </b><i><a class="txt" href="grcat_1.html#E3:97"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="grcat_1.html#E4:97"><i><font color="Green" title="E58">A2</font></i></a>, <a class="txt" href="grcat_1.html#E1:97_3"><i><font color="Green" title="E60">A4</font></i></a>, <a class="ref" href="grcat_1.html#T50" target="_self" title="GRCAT_1:th.50">Th50</a></i>
<br/>.= 
<font color="Maroon" title="c8">f</font>
<b>by </b><i><a class="txt" href="grcat_1.html#E4:97_3"><i><font color="Green" title="E61">A5</font></i></a>, <a class="ref" href="grcat_1.html#T34" target="_self" title="GRCAT_1:th.34">Th34</a></i>
; <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>thus </b><a NAME="E7:97"/>
for <font color="Olive" title="b1">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> holds <br/><font color="Olive" title="b1">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="grcat_1.html#K27" title="GRCAT_1:func.27">GroupCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> implies <font color="Maroon" title="c8">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font> )</span><br/>

<b>assume </b><a NAME="E1:97_4"/><i><font color="Green" title="E60">A6</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c8">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c9">f1</font> = <font color="Maroon" title="c8">f</font> as  <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>  <a href="grcat_1.html#M3" title="GRCAT_1:mode.3">Element</a> of  <a href="grcat_1.html#K19" title="GRCAT_1:func.19">Morphs</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K18" title="GRCAT_1:func.18">GroupObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span> <b>by </b><i><a class="ref" href="grcat_1.html#T47" target="_self" title="GRCAT_1:th.47">Th47</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">f'</font> = <font color="Maroon" title="c9">f1</font> as  <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a> <a href="grcat_1.html#NM1" title="GRCAT_1:NM.1">GroupMorphism</a> ;<br/>
<a NAME="E4:97_4"/><i><font color="Green" title="E61">A7</font></i>: 
 <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c10">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b''</font>
 
<b>by </b><i><a class="txt" href="grcat_1.html#E1:97_4"><i><font color="Green" title="E60">A6</font></i></a>, <a class="ref" href="grcat_1.html#T49" target="_self" title="GRCAT_1:th.49">Th49</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c8">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c5">b</font></span>)</span> = 
<font color="Maroon" title="c10">f'</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K12" title="GRCAT_1:func.12">ID</a> <font color="Maroon" title="c7">b''</font></span>)</span>
<b>by </b><i><a class="txt" href="grcat_1.html#E3:97"><i><font color="Green" title="E57">A1</font></i></a>, <a class="txt" href="grcat_1.html#E5:97"><i><font color="Green" title="E59">A3</font></i></a>, <a class="txt" href="grcat_1.html#E1:97_4"><i><font color="Green" title="E60">A6</font></i></a>, <a class="ref" href="grcat_1.html#T50" target="_self" title="GRCAT_1:th.50">Th50</a></i>
<br/>.= 
<font color="Maroon" title="c8">f</font>
<b>by </b><i><a class="txt" href="grcat_1.html#E4:97_4"><i><font color="Green" title="E61">A7</font></i></a>, <a class="ref" href="grcat_1.html#T34" target="_self" title="GRCAT_1:th.34">Th34</a></i>
; <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>


</div>
