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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>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">C</font> =  <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>;<br/>
<b>set </b><font color="Maroon" title="c4">V</font> =  <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>;<br/>
<b>set </b><font color="Maroon" title="c5">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="c6">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="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>let </b><font color="Maroon" title="c7">f'</font> be    <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>;<br/>



<b>assume </b><a NAME="E1:34"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f'</font>
 ;<br/>

<b>hence </b> <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c6">f</font> = 
<span class="p1">(<span class="default"><a href="modcat_1.html#K8" title="MODCAT_1:func.8">dom</a> <span class="p2">(<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></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f'</font>
<b>by </b><i><a class="ref" href="cat_1.html#D2" title="CAT_1:def.2">CAT_1:def 2</a></i>
<br/>.= 
 <a href="modcat_1.html#K5" title="MODCAT_1:func.5">dom'</a> <font color="Maroon" title="c7">f'</font>
<b>by </b><i><a class="ref" href="modcat_1.html#D11" target="_self" title="MODCAT_1:def.11">Def11</a></i>
<br/>.= 
 <a href="mod_2.html#K2" title="MOD_2:func.2">dom</a> <font color="Maroon" title="c7">f'</font>

;<br/><br/>

<b>thus </b> <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c6">f</font> = 
<span class="p1">(<span class="default"><a href="modcat_1.html#K9" title="MODCAT_1:func.9">cod</a> <span class="p2">(<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></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">f'</font>
<b>by </b><i><a class="txt" href="modcat_1.html#E1:34"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="cat_1.html#D3" title="CAT_1:def.3">CAT_1:def 3</a></i>
<br/>.= 
 <a href="modcat_1.html#K6" title="MODCAT_1:func.6">cod'</a> <font color="Maroon" title="c7">f'</font>
<b>by </b><i><a class="ref" href="modcat_1.html#D12" target="_self" title="MODCAT_1:def.12">Def12</a></i>
<br/>.= 
 <a href="mod_2.html#K3" title="MOD_2:func.3">cod</a> <font color="Maroon" title="c7">f'</font>

;<br/>


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