<?xml version="1.0"?>
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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <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> holds <br/> ( <font color="Olive" title="b1">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  is <a href="cat_1.html#V4" title="CAT_1:attr.4">monic</a> iff <font color="Olive" title="b1">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">epi</a> )</span><br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  is <a href="cat_1.html#V4" title="CAT_1:attr.4">monic</a> iff <font color="Maroon" title="c2">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">epi</a> )</span><br/>



<b>thus </b><a NAME="E1:16"/>
( <font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  is <a href="cat_1.html#V4" title="CAT_1:attr.4">monic</a> implies <font color="Maroon" title="c2">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">epi</a> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">epi</a> implies <font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  is <a href="cat_1.html#V4" title="CAT_1:attr.4">monic</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:16_1"/><i><font color="Green" title="E9">A1</font></i>: 
for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</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  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b2">f2</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b2">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Olive" title="b2">f2</font> holds <br/><font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">epi</a></span><br/>

<b>let </b><font color="Maroon" title="c3">g1</font>, <font color="Maroon" title="c4">g2</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D11" title="CAT_1:def.11">CAT_1:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font> or  not  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c4">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font> or  not  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c4">g2</font> or  not <font color="Maroon" title="c3">g1</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font> or <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E2:16_1"/><i><font color="Green" title="E10">A2</font></i>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c4">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font> )
 <b>and </b><br/><a NAME="E3:16_1"/><i><font color="Green" title="E11">A3</font></i>: 
(  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c4">g2</font> &amp; <font color="Maroon" title="c3">g1</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font></span><br/>

<a NAME="E4:16_1"/>
(  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">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#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</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#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">g1</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</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#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c4">g2</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</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">dom</a> <font color="Maroon" title="c3">g1</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</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">dom</a> <font color="Maroon" title="c4">g2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g1</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g2</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> &amp; <font color="Maroon" title="c3">g1</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g1</font> &amp; <font color="Maroon" title="c4">g2</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font> )
 
<b>by </b><i><a class="txt" href="oppcat_1.html#E2:16_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="oppcat_1.html#T17" target="_self" title="OPPCAT_1:th.17">Th17</a></i>;<br/>
<b>hence </b><a NAME="E5:16_1"/>
<font color="Maroon" title="c3">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g2</font>
 <b>by </b><i><a class="txt" href="oppcat_1.html#E1:16_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="oppcat_1.html#E2:16_1"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="oppcat_1.html#E3:16_1"><i><font color="Green" title="E11">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:16"/><i><font color="Green" title="E9">A4</font></i>: 
for <font color="Olive" title="b1">g1</font>, <font color="Olive" title="b2">g2</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b2">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b2">g2</font> &amp; <font color="Olive" title="b1">g1</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g2</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font> holds <br/><font color="Olive" title="b1">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g2</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D11" title="CAT_1:def.11">CAT_1:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  is <a href="cat_1.html#V4" title="CAT_1:attr.4">monic</a></span><br/>

<b>let </b><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <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>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c4">f2</font> or  not  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> or  not  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c4">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> or  not <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c4">f2</font> or <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E3:16"/><i><font color="Green" title="E10">A5</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c4">f2</font>
 <b>and </b><br/><a NAME="E4:16"/><i><font color="Green" title="E11">A6</font></i>: 
(  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c4">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> )
 <b>and </b><br/><a NAME="E5:16"/><i><font color="Green" title="E12">A7</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c4">f2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font></span><br/>

<b>set </b><font color="Maroon" title="c5">g1</font> =  <a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c3">f1</font>;<br/>
<b>set </b><font color="Maroon" title="c6">g2</font> =  <a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f2</font>;<br/>
<a NAME="E6:16"/><i><font color="Green" title="E13">A8</font></i>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">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#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font> )
 
;<br/>
<a NAME="E7:16"/><b>then </b>
(  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c3">f1</font></span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a> </span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f2</font></span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="oppcat_1.html#K6" title="OPPCAT_1:func.6">opp</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="oppcat_1.html#K5" title="OPPCAT_1:func.5">opp</a>  )
 
<b>by </b><i><a class="txt" href="oppcat_1.html#E4:16"><i><font color="Green" title="E11">A6</font></i></a>, <a class="ref" href="oppcat_1.html#T17" target="_self" title="OPPCAT_1:th.17">Th17</a></i>;<br/>
<b>hence </b><a NAME="E8:16"/>
<font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f2</font>
 <b>by </b><i><a class="txt" href="oppcat_1.html#E2:16"><i><font color="Green" title="E9">A4</font></i></a>, <a class="txt" href="oppcat_1.html#E3:16"><i><font color="Green" title="E10">A5</font></i></a>, <a class="txt" href="oppcat_1.html#E4:16"><i><font color="Green" title="E11">A6</font></i></a>, <a class="txt" href="oppcat_1.html#E5:16"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="oppcat_1.html#E6:16"><i><font color="Green" title="E13">A8</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
