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

<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>,<font color="Maroon" title="c3">C</font>;<br/>







<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 ;<br/>

<a NAME="E2:16"/><b>then </b><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></i>;<br/>
<b>let </b><font color="Maroon" title="c6">u</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font>;<br/><b>let </b><font color="Maroon" title="c7">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>;<br/>



<a NAME="E3:16"/>
the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">A</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="cat_2.html#T33" title="CAT_2:th.33">CAT_2:33</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c8">t</font> = <font color="Maroon" title="c6">u</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">A</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c3">C</font> ;<br/>
<a NAME="E5:16"/><i><font color="Green" title="E17">A3</font></i>: 
<font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a><br/>

<a NAME="E1:16_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c9">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c9">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> )
 
<b>by </b><i><a class="ref" href="isocat_2.html#T12" target="_self" title="ISOCAT_2:th.12">Th12</a></i>;<br/>
<b>hence </b><a NAME="E2:16_1"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="isocat_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green" title="E18">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font>;<br/><i><font color="Green" title="E19">A5</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</font> = 
<font color="Maroon" title="c8">t</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c9">b</font>
<b>by </b><i><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></i>
<br/>.= 
<font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c9">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
;<br/><a NAME="E2:16_2"/><i><font color="Green" title="E20">A6</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c9">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c9">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> )
 <b>by </b><i><a class="ref" href="isocat_2.html#T12" target="_self" title="ISOCAT_2:th.12">Th12</a></i>;<br/><a NAME="E3:16_2"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="isocat_2.html#E5:16"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/><b>hence </b><a NAME="E4:16_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:16_2"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="isocat_2.html#E2:16_2"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="cat_1.html#D7" title="CAT_1:def.7">CAT_1:def 7</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font>;<br/><a NAME="E1:16_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E6:16"><i><font color="Green" title="E18">A4</font></i></a></i>;<br/><b>hence </b><a NAME="E2:16_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b</font> is    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">b</font>
 <b>by </b><i><a class="ref" href="cat_1.html#D7" title="CAT_1:def.7">CAT_1:def 7</a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c9">s</font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font> as    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font> <b>by </b><i><a class="txt" href="isocat_2.html#E5:16"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="nattra_1.html#D3" title="NATTRA_1:def.3">NATTRA_1:def 3</a></i>;<br/>
<div><i><font color="Green" title="E19">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">b1</font>, <font color="Maroon" title="c11">b2</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font>;<br/><b>assume </b><a NAME="E1:16_4"/><i><font color="Green" title="E20">A8</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><b>let </b><font color="Maroon" title="c12">f</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">b2</font>;<br/><a NAME="E2:16_4"/><i><font color="Green" title="E21">A9</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c7">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="cat_1.html#T56" title="CAT_1:th.56">CAT_1:56</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c13">g</font> = <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c12">f</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> as    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> <b>by </b><i><a class="txt" href="isocat_2.html#E1:16_4"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="cat_2.html#T43" title="CAT_2:th.43">CAT_2:43</a></i>;<br/><a NAME="E4:16_4"/><i><font color="Green" title="E22">A10</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:16_4"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="isocat_2.html#E2:16_4"><i><font color="Green" title="E21">A9</font></i></a>, <a class="ref" href="isocat_2.html#T13" target="_self" title="ISOCAT_2:th.13">Th13</a></i>;<br/><a NAME="E5:16_4"/><b>then </b><i><font color="Green" title="E23">A11</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/><a NAME="E6:16_4"/><i><font color="Green" title="E24">A12</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="isocat_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/><a NAME="E7:16_4"/><i><font color="Green" title="E25">A13</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">b1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:16_4"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/><a NAME="E8:16_4"/><i><font color="Green" title="E26">A14</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> )
 <b>by </b><i><a class="ref" href="isocat_2.html#T12" target="_self" title="ISOCAT_2:th.12">Th12</a></i>;<br/><a NAME="E9:16_4"/><i><font color="Green" title="E27">A15</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="isocat_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/><a NAME="E10:16_4"/><i><font color="Green" title="E28">A16</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="isocat_2.html#E4:16_4"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/><a NAME="E11:16_4"/><i><font color="Green" title="E29">A17</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">b1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:16_4"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/><a NAME="E12:16_4"/><i><font color="Green" title="E30">A18</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> )
 <b>by </b><i><a class="ref" href="isocat_2.html#T12" target="_self" title="ISOCAT_2:th.12">Th12</a></i>;<br/><i><font color="Green" title="E31">A19</font></i>: <font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">b1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">b1</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E5:16"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
<br/>.= 
<font color="Maroon" title="c8">t</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font>
<b>by </b><i><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></i>
<br/>.= 
<font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
;<br/><font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">b2</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E5:16"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
<br/>.= 
<font color="Maroon" title="c8">t</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font>
<b>by </b><i><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></i>
<br/>.= 
<font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E2:16"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">b2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E6:16_4"><i><font color="Green" title="E24">A12</font></i></a>, <a class="txt" href="isocat_2.html#E7:16_4"><i><font color="Green" title="E25">A13</font></i></a>, <a class="txt" href="isocat_2.html#E8:16_4"><i><font color="Green" title="E26">A14</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:16_4"><i><font color="Green" title="E20">A8</font></i></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c12">f</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T47" title="CAT_2:th.47">CAT_2:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">g</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E4:16_4"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c11">b2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">g</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E5:16_4"><i><font color="Green" title="E23">A11</font></i></a>, <a class="txt" href="isocat_2.html#E6:16_4"><i><font color="Green" title="E24">A12</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">g</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:16"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="isocat_2.html#E4:16_4"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c13">g</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E9:16_4"><i><font color="Green" title="E27">A15</font></i></a>, <a class="txt" href="isocat_2.html#E10:16_4"><i><font color="Green" title="E28">A16</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c7">a</font></span>)</span>,<font color="Maroon" title="c12">f</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E4:16_4"><i><font color="Green" title="E22">A10</font></i></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c10">b1</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T47" title="CAT_2:th.47">CAT_2:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">b1</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:16_4"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="isocat_2.html#E13:16_4"><i><font color="Green" title="E31">A19</font></i></a>, <a class="ref" href="nattra_1.html#D1" title="NATTRA_1:def.1">NATTRA_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c12">f</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">b1</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E9:16_4"><i><font color="Green" title="E27">A15</font></i></a>, <a class="txt" href="isocat_2.html#E11:16_4"><i><font color="Green" title="E29">A17</font></i></a>, <a class="txt" href="isocat_2.html#E12:16_4"><i><font color="Green" title="E30">A18</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:16"/>
<font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E5:16"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></i>;<br/>

<b>hence </b><a NAME="E11:16"/>
<span class="p1">(<span class="default"><a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <font color="Maroon" title="c6">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">a</font> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E9:16"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a></i>;<br/>


</div>
