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<b>let </b><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</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="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c1">C</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">D</font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">f</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>thus </b><span class="p1">(<span class="default"><a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <span class="p2">(<span class="default"><a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">f</font> = 
<span class="p1">(<span class="default"><a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</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="c4">f</font> <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"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</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>
<b>by </b><i><a class="ref" href="oppcat_1.html#D8" target="_self" title="OPPCAT_1:def.8">Def8</a></i>
<br/>.= 
<font color="Maroon" title="c3">S</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">f</font>

;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:58"/>
 <a href="oppcat_1.html#K7" title="OPPCAT_1:func.7">/*</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">S</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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