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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="oppcat_1.html#M1" target="_self">Contravariant_Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>









<a NAME="E1:79"/>
 <a href="oppcat_1.html#K8" target="_self">*'</a> <font color="Maroon">c<sub>4</sub></font> is    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font> <a href="oppcat_1.html#K2" target="_self">opp</a> ,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="oppcat_1.html#T56" target="_self">Th56</a></i>;<br/>
<a NAME="E2:79"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K8" target="_self">*'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font> <a href="oppcat_1.html#K2" target="_self">opp</a> ,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="cat_1.html#T110">CAT_1:110</a></i>;<br/>
<a NAME="E3:79"/><b>then </b>
 <a href="oppcat_1.html#K7" target="_self">/*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="oppcat_1.html#K8" target="_self">*'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> is    <a href="oppcat_1.html#M1" target="_self">Contravariant_Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="oppcat_1.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E4:79"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K7" target="_self">/*</a> <span class="p2">(<span class="default"><a href="oppcat_1.html#K8" target="_self">*'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> is    <a href="oppcat_1.html#M1" target="_self">Contravariant_Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="oppcat_1.html#E76"><i><font color="Green">Lemma42</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:79"/>
<font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font> is    <a href="oppcat_1.html#M1" target="_self">Contravariant_Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="oppcat_1.html#T48" target="_self">Th48</a></i>;<br/>


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