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<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">F</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/>







<a NAME="E1:19"/>
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</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#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c1">A</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</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="c5">G</font> = <font color="Maroon" title="c4">F</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#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c1">A</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</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/>
<b>let </b><font color="Maroon" title="c6">a1</font>, <font color="Maroon" title="c7">a2</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>;<br/>

<b>assume </b><a NAME="E3:19"/><i><font color="Green" title="E17">A1</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c7">a2</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="c8">f</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c7">a2</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c9">Ff</font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c5">G</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c8">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">B</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c3">C</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c10">FfI</font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c8">f</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="cat_1.html#U6" title="CAT_1:sel.6">Id</a> of <font color="Maroon" title="c2">B</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c2">B</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c3">C</font> ;<br/>
<div><i><font color="Green" title="E18">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">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="E1:19_1"/><i><font color="Green" title="E19">A3</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</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="c6">a1</font>,<font color="Maroon" title="c11">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="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</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">a2</font>,<font color="Maroon" title="c11">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="E2:19_1"/>
( <font color="Maroon" title="c8">f</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> <font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c7">a2</font> &amp;  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c11">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> <font color="Maroon" title="c11">b</font>,<font color="Maroon" title="c11">b</font> )
 <b>by </b><i><a class="txt" href="isocat_2.html#E3:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="cat_1.html#T55" title="CAT_1:th.55">CAT_1:55</a>, <a class="ref" href="cat_1.html#D7" title="CAT_1:def.7">CAT_1:def 7</a></i>;<br/><a NAME="E3:19_1"/><b>then </b>
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c11">b</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <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"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c11">b</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">a2</font>,<font color="Maroon" title="c11">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#T16" target="_self" title="ISOCAT_2:th.16">Th16</a></i>;<br/><a NAME="E4:19_1"/><b>then </b>
<font color="Maroon" title="c4">F</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Maroon" title="c8">f</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c11">b</font></span>)</span> <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"><font color="Maroon" title="c4">F</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="c6">a1</font>,<font color="Maroon" title="c11">b</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">F</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">a2</font>,<font color="Maroon" title="c11">b</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_1.html#T123" title="CAT_1:th.123">CAT_1:123</a></i>;<br/><a NAME="E5:19_1"/><b>then </b>
<font color="Maroon" title="c9">Ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c11">b</font></span>)</span> <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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:19_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></i>;<br/><a NAME="E6:19_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c8">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c11">b</font></span>)</span> <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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>
 ;<br/><a NAME="E7:19_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c8">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U6" title="CAT_1:sel.6">Id</a> of <font color="Maroon" title="c2">B</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">b</font></span>)</span> <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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E8:19_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c8">f</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="cat_1.html#U6" title="CAT_1:sel.6">Id</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:19"/><i><font color="Green" title="E19">A4</font></i>: 
<font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c11">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/>

<b>thus </b><a NAME="E1:19_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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">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#E6:19"><i><font color="Green" title="E18">A2</font></i></a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">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="E1:19_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c8">f</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="cat_1.html#U6" title="CAT_1:sel.6">Id</a> of <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E6:19"><i><font color="Green" title="E18">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E2:19_3"/>
<font color="Maroon" title="c10">FfI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">b</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">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="c11">t</font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c8">f</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="cat_1.html#U6" title="CAT_1:sel.6">Id</a> of <font color="Maroon" title="c2">B</font> as    <a href="nattra_1.html#M1" title="NATTRA_1:mode.1">transformation</a> of <font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font> <b>by </b><i><a class="txt" href="isocat_2.html#E7:19"><i><font color="Green" title="E19">A4</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="E20">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">b1</font>, <font color="Maroon" title="c13">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="E1:19_4"/><i><font color="Green" title="E21">A6</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">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/><a NAME="E2:19_4"/><i><font color="Green" title="E22">A7</font></i>: 
(  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c6">a1</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>  &amp;  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c7">a2</font>,<font color="Maroon" title="c7">a2</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>  &amp;  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c12">b1</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>  &amp;  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c13">b2</font>,<font color="Maroon" title="c13">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>  )
 <b>by </b><i><a class="ref" href="cat_1.html#T56" title="CAT_1:th.56">CAT_1:56</a></i>;<br/><a NAME="E3:19_4"/><i><font color="Green" title="E23">A8</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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c12">b1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c12">b1</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#E7:19"><i><font color="Green" title="E19">A4</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="E4:19_4"/><i><font color="Green" title="E24">A9</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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c13">b2</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c13">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#E7:19"><i><font color="Green" title="E19">A4</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="E5:19_4"/><i><font color="Green" title="E25">A10</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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c12">b1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c13">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#E1:19_4"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/><a NAME="E6:19_4"/><i><font color="Green" title="E26">A11</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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c12">b1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c13">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#E1:19_4"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="cat_1.html#T126" title="CAT_1:th.126">CAT_1:126</a></i>;<br/><b>let </b><font color="Maroon" title="c14">g</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c12">b1</font>,<font color="Maroon" title="c13">b2</font>;<br/><a NAME="E7:19_4"/><i><font color="Green" title="E27">A12</font></i>: 
( <font color="Maroon" title="c11">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c13">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">FfI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">b2</font> &amp; <font color="Maroon" title="c11">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">FfI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">b1</font> )
 <b>by </b><i><a class="txt" href="isocat_2.html#E7:19"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c15">ida1</font> =  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c6">a1</font>, <font color="Maroon" title="c16">ida2</font> =  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c7">a2</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font> ;<br/><b>reconsider </b><font color="Maroon" title="c17">idb1</font> =  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c12">b1</font>, <font color="Maroon" title="c18">idb2</font> =  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c13">b2</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">B</font> ;<br/><i><font color="Green" title="E28">A13</font></i>:  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c7">a2</font></span>)</span> = 
<font color="Maroon" title="c7">a2</font>
<b>by </b><i><a class="ref" href="cat_1.html#T44" title="CAT_1:th.44">CAT_1:44</a></i>
<br/>.= 
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c8">f</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
;<br/><i><font color="Green" title="E29">A14</font></i>:  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c14">g</font> = 
<font color="Maroon" title="c12">b1</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:19_4"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
<br/>.= 
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c12">b1</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T44" title="CAT_1:th.44">CAT_1:44</a></i>
;<br/><i><font color="Green" title="E30">A15</font></i>:  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c6">a1</font></span>)</span> = 
<font color="Maroon" title="c6">a1</font>
<b>by </b><i><a class="ref" href="cat_1.html#T44" title="CAT_1:th.44">CAT_1:44</a></i>
<br/>.= 
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c8">f</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
;<br/><i><font color="Green" title="E31">A16</font></i>:  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c13">b2</font></span>)</span> = 
<font color="Maroon" title="c13">b2</font>
<b>by </b><i><a class="ref" href="cat_1.html#T44" title="CAT_1:th.44">CAT_1:44</a></i>
<br/>.= 
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c14">g</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:19_4"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
;<br/><i><font color="Green" title="E32">A17</font></i>:  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <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">a2</font></span>)</span>,<font color="Maroon" title="c14">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> = 
<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c8">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c14">g</font></span>)</span></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#E10:19_4"><i><font color="Green" title="E28">A13</font></i></a>, <a class="ref" href="cat_2.html#T38" title="CAT_2:th.38">CAT_2:38</a></i>
<br/>.= 
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c12">b1</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E11:19_4"><i><font color="Green" title="E29">A14</font></i></a>, <a class="ref" href="cat_2.html#T38" title="CAT_2:th.38">CAT_2:38</a></i>
;<br/><i><font color="Green" title="E33">A18</font></i>:  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <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="c6">a1</font></span>)</span>,<font color="Maroon" title="c14">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> = 
<span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c8">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c14">g</font></span>)</span></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#E12:19_4"><i><font color="Green" title="E30">A15</font></i></a>, <a class="ref" href="cat_2.html#T38" title="CAT_2:th.38">CAT_2:38</a></i>
<br/>.= 
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c13">b2</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E13:19_4"><i><font color="Green" title="E31">A16</font></i></a>, <a class="ref" href="cat_2.html#T38" title="CAT_2:th.38">CAT_2:38</a></i>
;<br/><i><font color="Green" title="E34">A19</font></i>: <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c15">ida1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c18">idb2</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c14">g</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> = 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c15">ida1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c13">b2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c14">g</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:19_4"><i><font color="Green" title="E21">A6</font></i></a>, <a class="txt" href="isocat_2.html#E2:19_4"><i><font color="Green" title="E22">A7</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"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c15">ida1</font></span>)</span>,<font color="Maroon" title="c14">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:19_4"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="cat_1.html#T57" title="CAT_1:th.57">CAT_1:57</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c6">a1</font></span>)</span></span>)</span>,<font color="Maroon" title="c14">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="isocat_2.html#E2:19_4"><i><font color="Green" title="E22">A7</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"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c14">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="cat_1.html#T58" title="CAT_1:th.58">CAT_1:58</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c8">f</font></span>)</span>,<font color="Maroon" title="c14">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="cat_1.html#T57" title="CAT_1:th.57">CAT_1:57</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">ida2</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c8">f</font></span>)</span>,<font color="Maroon" title="c14">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:19"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="isocat_2.html#E2:19_4"><i><font color="Green" title="E22">A7</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"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">ida2</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c8">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">g</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c12">b1</font></span>)</span></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:19_4"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="cat_1.html#T58" title="CAT_1:th.58">CAT_1:58</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">ida2</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c8">f</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c14">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c17">idb1</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:19_4"><i><font color="Green" title="E21">A6</font></i></a>, <a class="txt" href="isocat_2.html#E2:19_4"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c11">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c13">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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c14">g</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">FfI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">b2</font></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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c14">g</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E4:19_4"><i><font color="Green" title="E24">A9</font></i></a>, <a class="txt" href="isocat_2.html#E5:19_4"><i><font color="Green" title="E25">A10</font></i></a>, <a class="txt" href="isocat_2.html#E7:19_4"><i><font color="Green" title="E27">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="c9">Ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c13">b2</font></span>)</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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c14">g</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Maroon" title="c8">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c13">b2</font></span>)</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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c14">g</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f</font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c13">b2</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</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">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">g</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:19_4"><i><font color="Green" title="E21">A6</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="c4">F</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Maroon" title="c8">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c13">b2</font></span>)</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">F</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="c6">a1</font></span>)</span>,<font color="Maroon" title="c14">g</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/>.= 
<font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f</font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c13">b2</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c6">a1</font></span>)</span>,<font color="Maroon" title="c14">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E15:19_4"><i><font color="Green" title="E33">A18</font></i></a>, <a class="ref" href="cat_1.html#T99" title="CAT_1:th.99">CAT_1:99</a></i>
<br/>.= 
<font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">f</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c15">ida1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c18">idb2</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c14">g</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E12:19_4"><i><font color="Green" title="E30">A15</font></i></a>, <a class="txt" href="isocat_2.html#E13:19_4"><i><font color="Green" title="E31">A16</font></i></a>, <a class="ref" href="cat_2.html#T39" title="CAT_2:th.39">CAT_2:39</a></i>
<br/>.= 
<font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c16">ida2</font>,<font color="Maroon" title="c14">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c17">idb1</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E10:19_4"><i><font color="Green" title="E28">A13</font></i></a>, <a class="txt" href="isocat_2.html#E11:19_4"><i><font color="Green" title="E29">A14</font></i></a>, <a class="txt" href="isocat_2.html#E16:19_4"><i><font color="Green" title="E34">A19</font></i></a>, <a class="ref" href="cat_2.html#T39" title="CAT_2:th.39">CAT_2:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">F</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">a2</font></span>)</span>,<font color="Maroon" title="c14">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="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f</font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c12">b1</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E14:19_4"><i><font color="Green" title="E32">A17</font></i></a>, <a class="ref" href="cat_1.html#T99" title="CAT_1:th.99">CAT_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">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="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f</font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c12">b1</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</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="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c14">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="c4">F</font> <a href="cat_2.html#K14" title="CAT_2:func.14">.</a> <font color="Maroon" title="c8">f</font>,<span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c12">b1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:19_4"><i><font color="Green" title="E21">A6</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="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c14">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="c9">Ff</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c12">b1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c14">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="c10">FfI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">b1</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font></span>)</span> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c14">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="c11">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c12">b1</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:19_4"><i><font color="Green" title="E23">A8</font></i></a>, <a class="txt" href="isocat_2.html#E6:19_4"><i><font color="Green" title="E26">A11</font></i></a>, <a class="txt" href="isocat_2.html#E7:19_4"><i><font color="Green" title="E27">A12</font></i></a>, <a class="ref" href="cat_1.html#D13" title="CAT_1:def.13">CAT_1:def 13</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:19"/>
<font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E7:19"><i><font color="Green" title="E19">A4</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="E12:19"/>
<span class="p1">(<span class="default"><a href="isocat_2.html#K3" title="ISOCAT_2:func.3">curry</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c8">f</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="cat_1.html#U6" title="CAT_1:sel.6">Id</a> of <font color="Maroon" title="c2">B</font> is    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c6">a1</font>,<font color="Maroon" title="c4">F</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c7">a2</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E10:19"><i><font color="Green" title="E20">A5</font></i></a>, <a class="ref" href="nattra_1.html#D8" title="NATTRA_1:def.8">NATTRA_1:def 8</a></i>;<br/>


</div>
