<?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>;<br/><b>let </b><font color="Maroon" title="c2">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/>



<b>set </b><font color="Maroon" title="c3">X</font> =  <a href="modcat_1.html#K4" title="MODCAT_1:func.4">Morphs</a> <span class="p1">(<span class="default"><a href="modcat_1.html#K3" title="MODCAT_1:func.3">LModObjects</a> <font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font></span>)</span>;<br/>
<b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font>, <font color="Maroon" title="c6">h</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="modcat_1.html#K12" title="MODCAT_1:func.12">LModCat</a> <font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E29">A1</font></i>: 
(  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">g</font> &amp;  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c4">f</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c7">f'</font> = <font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c8">g'</font> = <font color="Maroon" title="c5">g</font>, <font color="Maroon" title="c9">h'</font> = <font color="Maroon" title="c6">h</font> as  <a href="mod_2.html#V2" title="MOD_2:attr.2">strict</a>  <a href="modcat_1.html#M4" title="MODCAT_1:mode.4">Element</a> of  <a href="modcat_1.html#K4" title="MODCAT_1:func.4">Morphs</a> <span class="p1">(<span class="default"><a href="modcat_1.html#K3" title="MODCAT_1:func.3">LModObjects</a> <font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font></span>)</span> <b>by </b><i><a class="ref" href="modcat_1.html#T15" target="_self" title="MODCAT_1:th.15">Th15</a></i>;<br/>
<a NAME="E3:37"/><i><font color="Green" title="E30">A2</font></i>: 
(  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c9">h'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c8">g'</font> &amp;  <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c8">g'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c7">f'</font> )
 
<b>by </b><i><a class="txt" href="modcat_1.html#E1:37"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="modcat_1.html#T18" target="_self" title="MODCAT_1:th.18">Th18</a></i>;<br/>
<a NAME="E4:37"/><i><font color="Green" title="E31">A3</font></i>: 
( <font color="Maroon" title="c8">g'</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c7">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c9">h'</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c8">g'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c5">g</font> )
 
<b>by </b><i><a class="txt" href="modcat_1.html#E1:37"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="modcat_1.html#T18" target="_self" title="MODCAT_1:th.18">Th18</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">gf</font> = <font color="Maroon" title="c8">g'</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c7">f'</font>, <font color="Maroon" title="c11">hg</font> = <font color="Maroon" title="c9">h'</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c8">g'</font> as  <a href="mod_2.html#V2" title="MOD_2:attr.2">strict</a>  <a href="modcat_1.html#M4" title="MODCAT_1:mode.4">Element</a> of  <a href="modcat_1.html#K4" title="MODCAT_1:func.4">Morphs</a> <span class="p1">(<span class="default"><a href="modcat_1.html#K3" title="MODCAT_1:func.3">LModObjects</a> <font color="Maroon" title="c1">UN</font>,<font color="Maroon" title="c2">R</font></span>)</span> <b>by </b><i><a class="txt" href="modcat_1.html#E3:37"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="modcat_1.html#T12" target="_self" title="MODCAT_1:th.12">Th12</a></i>;<br/>
<a NAME="E6:37"/><i><font color="Green" title="E32">A4</font></i>: 
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c6">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c4">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="modcat_1.html#E1:37"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="modcat_1.html#E34"><i><font color="Green" title="E27">Lm1</font></i></a></i>;<br/>
<a NAME="E7:37"/><i><font color="Green" title="E33">A5</font></i>: 
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="modcat_1.html#E1:37"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="modcat_1.html#E34"><i><font color="Green" title="E27">Lm1</font></i></a></i>;<br/>
<font color="Maroon" title="c6">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c4">f</font></span>)</span> = 
<font color="Maroon" title="c9">h'</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c10">gf</font>
<b>by </b><i><a class="txt" href="modcat_1.html#E4:37"><i><font color="Green" title="E31">A3</font></i></a>, <a class="txt" href="modcat_1.html#E6:37"><i><font color="Green" title="E32">A4</font></i></a>, <a class="ref" href="modcat_1.html#T18" target="_self" title="MODCAT_1:th.18">Th18</a></i>
<br/>.= 
<font color="Maroon" title="c11">hg</font> <a href="mod_2.html#K8" title="MOD_2:func.8">*</a> <font color="Maroon" title="c7">f'</font>
<b>by </b><i><a class="txt" href="modcat_1.html#E3:37"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="mod_2.html#T25" title="MOD_2:th.25">MOD_2:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c4">f</font>
<b>by </b><i><a class="txt" href="modcat_1.html#E4:37"><i><font color="Green" title="E31">A3</font></i></a>, <a class="txt" href="modcat_1.html#E7:37"><i><font color="Green" title="E33">A5</font></i></a>, <a class="ref" href="modcat_1.html#T18" target="_self" title="MODCAT_1:th.18">Th18</a></i>
;<br/>
<b>hence </b><a NAME="E9:37"/>
<font color="Maroon" title="c6">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">h</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c4">f</font>
 ;<br/>


</div>
