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

<b>let </b><font color="Maroon">A</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="cat_1.html#M2">Functor</a> of <span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="cat_2.html#K11">:]</a></span>,<font color="Maroon">C</font>;<br/>







<a NAME="E1:20"/>
the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="cat_2.html#K11">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">A</font>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="cat_2.html#T33">CAT_2:33</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">G</font> = <font color="Maroon">F</font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">A</font>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> ;<br/>
<b>let </b><font color="Maroon">a1</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>, <font color="Maroon">a2</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>;<br/>

<b>assume </b><a NAME="E3:20"/><i><font color="Green">E16</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a1</font>,<font color="Maroon">a2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>let </b><font color="Maroon">f</font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">a1</font>,<font color="Maroon">a2</font>;<br/>

<b>reconsider </b><font color="Maroon">Ff</font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2">curry</a> <font color="Maroon">G</font></span>)</span> <a href="cat_2.html#K1">.</a> <font color="Maroon">f</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">B</font>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> ;<br/>
<b>reconsider </b><font color="Maroon">FfI</font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">B</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">B</font>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> ;<br/>
<div><i><font color="Green">E17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>;<br/><a NAME="E1:20_1"/><i><font color="Green">E32</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">b</font></span><a href="cat_2.html#K12">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">a2</font>,<font color="Maroon">b</font></span><a href="cat_2.html#K12">]</a></span> )
 <b>by </b><i/>;<br/><a NAME="E2:20_1"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a1</font>,<font color="Maroon">a2</font> &amp;  <a href="cat_1.html#K10">id</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="isocat_2.html#T1" target="_self">Th1</a>, <a class="ref" href="cat_1.html#T55">CAT_1:55</a>, <a class="ref" href="cat_1.html#D7">CAT_1:def 7</a></i>;<br/><a NAME="E3:20_1"/><b>then </b>
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span></span><a href="cat_2.html#K13">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">b</font></span><a href="cat_2.html#K12">]</a></span>,<span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">a2</font>,<font color="Maroon">b</font></span><a href="cat_2.html#K12">]</a></span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E3:20"><i><font color="Green">E16</font></i></a></i>;<br/><a NAME="E4:20_1"/><b>then </b>
<font color="Maroon">F</font> <a href="cat_2.html#K14">.</a> <font color="Maroon">f</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">b</font></span><a href="cat_2.html#K12">]</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">a2</font>,<font color="Maroon">b</font></span><a href="cat_2.html#K12">]</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#T123">CAT_1:123</a></i>;<br/><a NAME="E5:20_1"/><b>then </b>
<font color="Maroon">Ff</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="cat_2.html#T3">CAT_2:3</a></i>;<br/><a NAME="E6:20_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>
 ;<br/><a NAME="E7:20_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">B</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#D5">CAT_1:def 5</a></i>;<br/><b>hence </b><a NAME="E8:20_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:20"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a><br/>

<b>thus </b><a NAME="E1:20_2"/>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="isocat_2.html#T2" target="_self">Th2</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>;<br/><a NAME="E1:20_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="isocat_2.html#T2" target="_self">Th2</a></i>;<br/><b>hence </b><a NAME="E2:20_3"/>
<font color="Maroon">FfI</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b</font> is    <a href="cat_1.html#M1">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="cat_1.html#D7">CAT_1:def 7</a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">t</font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">B</font> as    <a href="nattra_1.html#M1">transformation</a> of <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font>,<font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font> <b>by </b><i>, <a class="ref" href="nattra_1.html#D3">NATTRA_1:def 3</a></i>;<br/>
<div><i><font color="Green">E50</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">b1</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>, <font color="Maroon">b2</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>;<br/><b>assume </b><a NAME="E1:20_4"/><i><font color="Green">E51</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:20_4"/><i><font color="Green">E54</font></i>: 
(  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a1</font>,<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a2</font>,<font color="Maroon">a2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">b1</font>,<font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">b2</font>,<font color="Maroon">b2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="ref" href="cat_1.html#T56">CAT_1:56</a></i>;<br/><a NAME="E3:20_4"/><i><font color="Green">E55</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b1</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/><a NAME="E4:20_4"/><i><font color="Green">E57</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b2</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/><a NAME="E5:20_4"/><i><font color="Green">E58</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b2</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, <a class="ref" href="cat_1.html#T126">CAT_1:126</a></i>;<br/><a NAME="E6:20_4"/><i><font color="Green">E59</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">b2</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, <a class="ref" href="cat_1.html#T126">CAT_1:126</a></i>;<br/><b>let </b><font color="Maroon">g</font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">b1</font>,<font color="Maroon">b2</font>;<br/><a NAME="E7:20_4"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">t</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">FfI</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b2</font> &amp; <font color="Maroon">t</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">FfI</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b1</font> )
 <b>by </b><i>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">ida1</font> =  <a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font>, <font color="Maroon">ida2</font> =  <a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">A</font> ;<br/><b>reconsider </b><font color="Maroon">idb1</font> =  <a href="cat_1.html#K10">id</a> <font color="Maroon">b1</font>, <font color="Maroon">idb2</font> =  <a href="cat_1.html#K10">id</a> <font color="Maroon">b2</font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">B</font> ;<br/><i><font color="Green">E61</font></i>:  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font></span>)</span> = 
<font color="Maroon">a2</font>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
<br/>.= 
 <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="isocat_2.html#T1" target="_self">Th1</a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
;<br/><i><font color="Green">E62</font></i>:  <a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font> = 
<font color="Maroon">b1</font>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
<br/>.= 
 <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b1</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
;<br/><i><font color="Green">E65</font></i>:  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font></span>)</span> = 
<font color="Maroon">a1</font>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
<br/>.= 
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="isocat_2.html#T1" target="_self">Th1</a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
;<br/><i><font color="Green">E66</font></i>:  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b2</font></span>)</span> = 
<font color="Maroon">b2</font>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
<br/>.= 
 <a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
;<br/><i><font color="Green">E67</font></i>:  <a href="cat_1.html#K2">dom</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font></span>)</span>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span> = 
<span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span><a href="cat_2.html#K12">]</a></span>
<b>by </b><i>, <a class="ref" href="cat_2.html#T38">CAT_2:38</a></i>
<br/>.= 
 <a href="cat_1.html#K3">cod</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b1</font></span>)</span></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i>, <a class="ref" href="cat_2.html#T38">CAT_2:38</a></i>
;<br/><i><font color="Green">E68</font></i>:  <a href="cat_1.html#K3">cod</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font></span>)</span>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span> = 
<span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span><a href="cat_2.html#K12">]</a></span>
<b>by </b><i>, <a class="ref" href="cat_2.html#T38">CAT_2:38</a></i>
<br/>.= 
 <a href="cat_1.html#K2">dom</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b2</font></span>)</span></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i>, <a class="ref" href="cat_2.html#T38">CAT_2:38</a></i>
;<br/><i><font color="Green">E69</font></i>: <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">ida1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">idb2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g</font></span>)</span></span><a href="cat_2.html#K13">]</a></span> = 
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">ida1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b2</font></span>)</span> <a href="cat_1.html#K9">*</a> <font color="Maroon">g</font></span>)</span></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, , <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">ida1</font></span>)</span>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, <a class="ref" href="cat_1.html#T57">CAT_1:57</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cat_1.html#K9">*</a> <span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font></span>)</span></span>)</span>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="ref" href="isocat_2.html#T1" target="_self">Th1</a>, , <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="ref" href="isocat_2.html#T1" target="_self">Th1</a>, <a class="ref" href="cat_1.html#T58">CAT_1:58</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font></span>)</span> <a href="cat_1.html#K9">*</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="ref" href="isocat_2.html#T1" target="_self">Th1</a>, <a class="ref" href="cat_1.html#T57">CAT_1:57</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">ida2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="ref" href="isocat_2.html#T1" target="_self">Th1</a>, , <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">ida2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K9">*</a> <span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b1</font></span>)</span></span>)</span></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, <a class="ref" href="cat_1.html#T58">CAT_1:58</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">ida2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">idb1</font></span>)</span></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, , <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b2</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">g</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">FfI</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i>, <a class="ref" href="isocat_2.html#T4" target="_self">Th4</a>, , <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default">the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">B</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">Ff</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#D5">CAT_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K14">.</a> <font color="Maroon">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3">CAT_2:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b2</font></span>)</span></span><a href="cat_2.html#K13">]</a></span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, <a class="ref" href="nattra_1.html#D1">NATTRA_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K14">.</a> <font color="Maroon">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K14">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font></span>)</span>,<font color="Maroon">g</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T47">CAT_2:47</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b2</font></span>)</span></span><a href="cat_2.html#K13">]</a></span> <a href="cat_1.html#K4">*</a> <span class="p2"><a href="cat_2.html#K13">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font></span>)</span>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T99">CAT_1:99</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">ida1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">idb2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g</font></span>)</span></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i>, , <a class="ref" href="cat_2.html#T39">CAT_2:39</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">ida2</font>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span> <a href="cat_1.html#K4">*</a> <span class="p2"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">idb1</font></span><a href="cat_2.html#K13">]</a></span></span>)</span>
<b>by </b><i>, , , <a class="ref" href="cat_2.html#T39">CAT_2:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K14">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font></span>)</span>,<font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b1</font></span>)</span></span><a href="cat_2.html#K13">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E7:20"><i><font color="Green">E33</font></i></a>, <a class="ref" href="cat_1.html#T99">CAT_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b1</font></span>)</span></span><a href="cat_2.html#K13">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T47">CAT_2:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K14">.</a> <font color="Maroon">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, <a class="ref" href="nattra_1.html#D1">NATTRA_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">Ff</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3">CAT_2:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default">the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">B</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#D5">CAT_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">FfI</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b1</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font></span>)</span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="isocat_2.html#T5" target="_self">Th5</a>, , <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:20"/>
<font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font>
 <b>by </b><i>, <a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/>

<b>hence </b><a NAME="E12:20"/>
<span class="p1">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">B</font> is    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a1</font>,<font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">a2</font>
 <b>by </b><i>, <a class="ref" href="nattra_1.html#D8">NATTRA_1:def 8</a></i>;<br/>


</div>
