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<b>let </b><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">B</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c3">S</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a> ,<font color="Maroon" title="c2">B</font>;<br/><b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>;<br/>







<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E18">A1</font></i>: 
 <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/>

<a NAME="E2:30"/><i><font color="Green" title="E19">A2</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="c4">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </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> &amp;  <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="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">g</font> )
 
;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</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="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<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="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span>
<b>by </b><i><a class="ref" href="oppcat_1.html#D6" target="_self" title="OPPCAT_1:def.6">Def6</a></i>
<br/>.= 
<font color="Maroon" title="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="oppcat_1.html#E1:30"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="oppcat_1.html#T17" target="_self" title="OPPCAT_1:th.17">Th17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="oppcat_1.html#E1:30"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="oppcat_1.html#E2:30"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="cat_1.html#T99" title="CAT_1:th.99">CAT_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="oppcat_1.html#D6" target="_self" title="OPPCAT_1:def.6">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">g</font></span>)</span>
<b>by </b><i><a class="ref" href="oppcat_1.html#D6" target="_self" title="OPPCAT_1:def.6">Def6</a></i>
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