<?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/><b>let </b><font color="Maroon">g</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">A</font>, <font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">A</font>;<br/>









<b>assume </b><a NAME="E1:25"/><i><font color="Green">E16</font></i>: 
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font>
 ;<br/>

<b>let </b><font color="Maroon">t</font> be    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:25"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">t</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">F</font> <a href="isocat_2.html#K4" target="_self">?-</a> <font color="Maroon">f</font>
 ;<br/>

<a NAME="E3:25"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span> &amp; <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</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="isocat_2.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E4:25"/><b>then </b><i><font color="Green">E33</font></i>: 
( <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span> &amp; <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/>
<a NAME="E5:25"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nattra_1.html#T19">NATTRA_1:19</a></i>;<br/>
<a NAME="E6:25"/>
<font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="isocat_2.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E7:25"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/>
<a NAME="E8:25"/><i><font color="Green">E54</font></i>: 
(  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font> &amp;  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font> )
 
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, <a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>;<br/>
<b>reconsider </b><font color="Maroon">s</font> = <font color="Maroon">t</font> as    <a href="nattra_1.html#M1">transformation</a> of <font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">F</font> <a href="cat_2.html#K15">?-</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span> ;<br/>
<a NAME="E10:25"/>
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>reconsider </b><font color="Maroon">Fgf</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> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span>, <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>, <font color="Maroon">Fg</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">g</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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_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/><i><font color="Green">E55</font></i>: <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="isocat_2.html#K4" target="_self">?-</a> <font color="Maroon">g</font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b</font> = 
<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">g</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>
<b>by </b><i>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<font color="Maroon">g</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>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon">Fg</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>
<b>by </b><i><a class="ref" href="cat_1.html#D5">CAT_1:def 5</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="cat_2.html#K14">.</a> <font color="Maroon">g</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</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/><i><font color="Green">E57</font></i>: <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="isocat_2.html#K4" target="_self">?-</a> <font color="Maroon">f</font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b</font> = 
<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>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, , <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
<br/>.= 
<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>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
<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>
<b>by </b><i><a class="ref" href="cat_1.html#D5">CAT_1:def 5</a></i>
<br/>.= 
<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>
<b>by </b><i><a class="ref" href="cat_2.html#T3">CAT_2:3</a></i>
;<br/> <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">b</font></span>)</span> = 
<font color="Maroon">b</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> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
;<br/><b>then </b><i><font color="Green">E58</font></i>:  <a href="cat_1.html#K2">dom</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">g</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> = 
<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#K3">cod</a> <span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span></span>)</span></span><a href="cat_2.html#K12">]</a></span>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</a>, <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">b</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/><a NAME="E5:25_1"/><i><font color="Green">E59</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">b</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="E6:25_1"/><i><font color="Green">E60</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> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></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> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></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>  &amp;  <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> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></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> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></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="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="isocat_2.html#K4" target="_self">?-</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b</font> = 
<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>,<span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span></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>
<b>by </b><i><a class="ref" href="isocat_2.html#T5" target="_self">Th5</a>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="isocat_2.html#K3" target="_self">curry</a> <font color="Maroon">F</font>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span></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>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon">Fgf</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>
<b>by </b><i><a class="ref" href="cat_1.html#D5">CAT_1:def 5</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="cat_2.html#K14">.</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</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/>.= 
<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">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</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">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span></span>)</span></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="ref" href="cat_1.html#T59">CAT_1:59</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">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</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">b</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span></span>)</span></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:25"><i><font color="Green">E32</font></i></a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</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">g</font>,<span class="p3">(<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="cat_1.html#K4">*</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">b</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#T40">CAT_2:40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="isocat_2.html#K4" target="_self">?-</a> <font color="Maroon">g</font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="isocat_2.html#T3" target="_self">Th3</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="isocat_2.html#K4" target="_self">?-</a> <font color="Maroon">g</font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E4:25"><i><font color="Green">E33</font></i></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"><font color="Maroon">F</font> <a href="isocat_2.html#K4" target="_self">?-</a> <font color="Maroon">g</font></span>)</span> <a href="nattra_1.html#K6">`*`</a> <font color="Maroon">s</font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">b</font>
<b>by </b><i>, <a class="ref" href="nattra_1.html#D6">NATTRA_1:def 6</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E14:25"/><b>then </b>
<font color="Maroon">F</font> <a href="isocat_2.html#K4" target="_self">?-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="isocat_2.html#K4" target="_self">?-</a> <font color="Maroon">g</font></span>)</span> <a href="nattra_1.html#K6">`*`</a> <font color="Maroon">s</font>
 
<b>by </b><i><a class="ref" href="isocat_2.html#T4" target="_self">Th4</a>, , <a class="ref" href="nattra_1.html#T20">NATTRA_1:20</a></i>;<br/>
<b>hence </b><a NAME="E15:25"/>
<font color="Maroon">F</font> <a href="isocat_2.html#K4" target="_self">?-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="isocat_2.html#K4" target="_self">?-</a> <font color="Maroon">g</font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="nattra_1.html#D9">NATTRA_1:def 9</a></i>;<br/>


</div>
