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<b>let </b><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>;<br/>

<b>set </b><font color="Maroon" title="c2">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="c3">f</font>, <font color="Maroon" title="c4">g</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>;<br/>

<b>assume </b><a NAME="E1:95"/><i><font color="Green" title="E55">A1</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c5">f'</font> = <font color="Maroon" title="c3">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="c6">g'</font> = <font color="Maroon" title="c4">g</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/>
<a NAME="E4:95"/><i><font color="Green" title="E56">A2</font></i>: 
 <a href="grcat_1.html#K20" title="GRCAT_1:func.20">dom</a> <font color="Maroon" title="c6">g'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K21" title="GRCAT_1:func.21">cod</a> <font color="Maroon" title="c5">f'</font>
 
<b>by </b><i><a class="txt" href="grcat_1.html#E1:95"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="grcat_1.html#T50" target="_self" title="GRCAT_1:th.50">Th50</a></i>;<br/>
<a NAME="E5:95"/><b>then </b><i><font color="Green" title="E57">A3</font></i>: 
(  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g'</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K20" title="GRCAT_1:func.20">dom</a> <font color="Maroon" title="c5">f'</font> &amp;  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g'</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K21" title="GRCAT_1:func.21">cod</a> <font color="Maroon" title="c6">g'</font> )
 
<b>by </b><i><a class="ref" href="grcat_1.html#T31" target="_self" title="GRCAT_1:th.31">Th31</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">gf</font> = <font color="Maroon" title="c6">g'</font> <a href="grcat_1.html#K14" title="GRCAT_1:func.14">*</a> <font color="Maroon" title="c5">f'</font> as    <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="txt" href="grcat_1.html#E4:95"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="grcat_1.html#T45" target="_self" title="GRCAT_1:th.45">Th45</a></i>;<br/>
<a NAME="E7:95"/>
<font color="Maroon" title="c7">gf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font>
 
<b>by </b><i><a class="txt" href="grcat_1.html#E1:95"><i><font color="Green" title="E55">A1</font></i></a>, <a class="ref" href="grcat_1.html#T50" target="_self" title="GRCAT_1:th.50">Th50</a></i>;<br/>
<b>hence </b><a NAME="E8:95"/>
(  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c3">f</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c4">g</font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E5:95"><i><font color="Green" title="E57">A3</font></i></a>, <a class="ref" href="grcat_1.html#T50" target="_self" title="GRCAT_1:th.50">Th50</a></i>;<br/>


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