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

<span class="kw">let </span><font color="Maroon" title="c1">C</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="firebrick">::  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 <br/> ( <font color="Olive" title="b1">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a>  is  <a href="cat_1.html#V7" title="CAT_1:attr.7">initial</a>  iff <font color="Olive" title="b1">c</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a>  is  <a href="cat_1.html#V7" title="CAT_1:attr.7">initial</a>  iff <font color="Maroon" title="c2">c</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a>  )</span><br/>



<span class="kw">thus </span><a NAME="E1:20"/>
( <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a>  is  <a href="cat_1.html#V7" title="CAT_1:attr.7">initial</a>  implies <font color="Maroon" title="c2">c</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a>  )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">c</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a>  implies <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a>  is  <a href="cat_1.html#V7" title="CAT_1:attr.7">initial</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:20_1"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a>  is  <a href="cat_1.html#V7" title="CAT_1:attr.7">initial</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">c</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_1.html#D12" title="CAT_1:def.12">CAT_1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  ex <font color="Olive">b<sub>1</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font> st <br/> for <font color="Olive">b<sub>2</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font> holds  <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c4">f</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> ,<font color="Maroon" title="c3">b</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> <span class="kw"> such that </span><br/><a NAME="E3:20_1"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
 for <font color="Olive" title="b1">g</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> ,<font color="Maroon" title="c3">b</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a>  holds  <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>;<br/>
<a NAME="E4:20_1"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
(  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</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> <font color="Maroon" title="c3">b</font> &amp;  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">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> <font color="Maroon" title="c2">c</font> )
 
;<br/>
<a NAME="E5:20_1"/><span class="lab"><font color="Green" title="E12">A4</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">f9</font> =  <a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f</font> as    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="oppcat_1.html#T15" target="_self" title="OPPCAT_1:th.15">Th16</a></span>;<br/>
<a NAME="E7:20_1"/>
 ex <font color="Olive" title="b1">f</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span> st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:20_1"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="ref" href="subset_1.html#T4" title="SUBSET_1:th.4">SUBSET_1:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:20_1"/><span class="lab"><font color="Green" title="E13">A5</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20_1"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="oppcat_1.html#T13" target="_self" title="OPPCAT_1:th.13">Th14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font> st <br/> for <font color="Olive">b<sub>2</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font> holds  <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c5">f9</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font> holds  <font color="Maroon" title="c5">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">g</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font></span><br/>

<a NAME="E9:20_1"/>
<font color="Maroon" title="c6">g</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> ,<font color="Maroon" title="c3">b</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:20_1"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="ref" href="oppcat_1.html#T14" target="_self" title="OPPCAT_1:th.14">Th15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:20_1"/>
<font color="Maroon" title="c5">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:20_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:20"/><span class="lab"><font color="Green" title="E9">A6</font></span>: 
<font color="Maroon" title="c2">c</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a>  is  <a href="cat_1.html#V7" title="CAT_1:attr.7">initial</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="oppcat_1.html#K2" title="OPPCAT_1:func.2">opp</a></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a></span>)</span>,<font color="Maroon" title="c3">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  ex <font color="Olive">b<sub>1</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> ,<font color="Maroon" title="c3">b</font> st <br/> for <font color="Olive">b<sub>2</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> ,<font color="Maroon" title="c3">b</font> holds  <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c4">f</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font><span class="kw"> such that </span><br/><a NAME="E4:20"/><span class="lab"><font color="Green" title="E10">A7</font></span>: 
 for <font color="Olive" title="b1">g</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">c</font> holds  <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="ref" href="cat_1.html#D12" title="CAT_1:def.12">CAT_1:def 12</a></span>;<br/>
<a NAME="E5:20"/><span class="lab"><font color="Green" title="E11">A8</font></span>: 
<span class="p1">(<span class="default"><a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font>
 
;<br/>
<a NAME="E6:20"/><span class="lab"><font color="Green" title="E12">A9</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">c</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="ref" href="cat_1.html#D12" title="CAT_1:def.12">CAT_1:def 12</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">f9</font> = <font color="Maroon" title="c4">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  as    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> ,<font color="Maroon" title="c3">b</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="ref" href="oppcat_1.html#T14" target="_self" title="OPPCAT_1:th.14">Th15</a></span>;<br/>
<a NAME="E8:20"/>
 ex <font color="Olive" title="b1">f</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c3">b</font></span>)</span>,<font color="Maroon" title="c2">c</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E12">A9</font></span></a>, <a class="ref" href="subset_1.html#T4" title="SUBSET_1:th.4">SUBSET_1:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:20"/><span class="lab"><font color="Green" title="E13">A10</font></span>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a></span>)</span>,<font color="Maroon" title="c3">b</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="ref" href="oppcat_1.html#T12" target="_self" title="OPPCAT_1:th.12">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> ,<font color="Maroon" title="c3">b</font> st <br/> for <font color="Olive">b<sub>2</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> ,<font color="Maroon" title="c3">b</font> holds  <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>2</sub></font></span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c5">f9</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> ,<font color="Maroon" title="c3">b</font> holds  <font color="Maroon" title="c5">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">g</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a> ,<font color="Maroon" title="c3">b</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font></span><br/>

<a NAME="E10:20"/>
 <a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c6">g</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of  <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <font color="Maroon" title="c3">b</font>, <a href="oppcat_1.html#K4" title="OPPCAT_1:func.4">opp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">c</font> <a href="oppcat_1.html#K3" title="OPPCAT_1:func.3">opp</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:20"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="ref" href="oppcat_1.html#T15" target="_self" title="OPPCAT_1:th.15">Th16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:20"/>
<font color="Maroon" title="c5">f9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E10">A7</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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