<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">D</font><br/> for <font color="Olive" title="b2">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="oppcat_1.html#K9" title="OPPCAT_1:func.9">*'</a> </span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">c</font></span>)</span> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">D</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> holds  <span class="p1">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="oppcat_1.html#K9" title="OPPCAT_1:func.9">*'</a> </span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">c</font></span>)</span> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">c</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="oppcat_1.html#K9" title="OPPCAT_1:func.9">*'</a> </span>)</span></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">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> </span><br/>







<a NAME="E1:82"/>
 <a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <font color="Maroon" title="c3">F</font> is    <a href="oppcat_1.html#M1" title="OPPCAT_1:mode.1">Contravariant_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">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="oppcat_1.html#T58" target="_self" title="OPPCAT_1:th.58">Th58</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="oppcat_1.html#K9" title="OPPCAT_1:func.9">*'</a> </span>)</span></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">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <span class="p3">(<span class="default"><a href="oppcat_1.html#K8" title="OPPCAT_1:func.8">*'</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> </span>)</span></span>)</span> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="oppcat_1.html#T46" target="_self" title="OPPCAT_1:th.46">Th46</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> </span>)</span></span>)</span></span>)</span> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="oppcat_1.html#T41" target="_self" title="OPPCAT_1:th.41">Th41</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K8" title="CAT_1:func.8">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> 

;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
