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<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>, <font color="Maroon" title="c6">F3</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><b>that </b><br/><a NAME="E1:33"/><i><font color="Green" title="E30">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>
 <b>and </b><br/><a NAME="E2:33"/><i><font color="Green" title="E31">A2</font></i>: 
<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F3</font>
 ;<br/>

<a NAME="E3:33"/><i><font color="Green" title="E32">A3</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="c6">F3</font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E1:33"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="isocat_2.html#E2:33"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="nattra_1.html#T25" title="NATTRA_1:th.25">NATTRA_1:25</a></i>;<br/>
<a NAME="E4:33"/><i><font color="Green" title="E33">A4</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="txt" href="isocat_2.html#E1:33"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></i>;<br/>
<a NAME="E5:33"/><i><font color="Green" title="E34">A5</font></i>: 
<font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c6">F3</font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E2:33"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></i>;<br/>
<a NAME="E6:33"/><i><font color="Green" title="E35">A6</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="c6">F3</font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:33"><i><font color="Green" title="E32">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>let </b><font color="Maroon" title="c7">t1</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="c8">t2</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c5">F2</font>,<font color="Maroon" title="c6">F3</font>;<br/>



<a NAME="E7:33"/><i><font color="Green" title="E36">A7</font></i>: 
 <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a>  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E1:33"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="isocat_2.html#T27" target="_self" title="ISOCAT_2:th.27">Th27</a></i>;<br/>
<a NAME="E8:33"/><b>then </b><i><font color="Green" title="E37">A8</font></i>: 
 <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a>  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</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/>
<a NAME="E9:33"/><i><font color="Green" title="E38">A9</font></i>: 
 <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a>  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c6">F3</font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E2:33"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="isocat_2.html#T27" target="_self" title="ISOCAT_2:th.27">Th27</a></i>;<br/>
<a NAME="E10:33"/><b>then </b><i><font color="Green" title="E39">A10</font></i>: 
 <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a>  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c6">F3</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/>
<a NAME="E11:33"/><b>then </b><i><font color="Green" title="E40">A11</font></i>: 
 <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a>  <a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c6">F3</font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E8:33"><i><font color="Green" title="E37">A8</font></i></a>, <a class="ref" href="nattra_1.html#T19" title="NATTRA_1:th.19">NATTRA_1:19</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c9">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="E1:33_1"/>
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</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="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">A</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</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="c10">s1</font> = <font color="Maroon" title="c7">t1</font>, <font color="Maroon" title="c11">s2</font> = <font color="Maroon" title="c8">t2</font>, <font color="Maroon" title="c12">s3</font> = <font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c7">t1</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="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">A</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</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="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c3">C</font> ;<br/><b>reconsider </b><font color="Maroon" title="c13">S1</font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c14">S2</font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c15">S3</font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c6">F3</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font> as    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font> <b>by </b><i><a class="ref" href="isocat_2.html#T8" target="_self" title="ISOCAT_2:th.8">Th8</a></i>;<br/><a NAME="E4:33_1"/><i><font color="Green" title="E41">A12</font></i>: 
( <font color="Maroon" title="c13">S1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">F1</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c9">a</font> &amp; <font color="Maroon" title="c14">S2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c9">a</font> &amp; <font color="Maroon" title="c15">S3</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c6">F3</font> <a href="cat_2.html#K15" title="CAT_2:func.15">?-</a> <font color="Maroon" title="c9">a</font> )
 <b>by </b><i><a class="ref" href="isocat_2.html#T24" target="_self" title="ISOCAT_2:th.24">Th24</a></i>;<br/><a NAME="E5:33_1"/><b>then </b><i><font color="Green" title="E42">A13</font></i>: 
<font color="Maroon" title="c13">S1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c14">S2</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:33"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="isocat_2.html#T15" target="_self" title="ISOCAT_2:th.15">Th15</a></i>;<br/><a NAME="E6:33_1"/><i><font color="Green" title="E43">A14</font></i>: 
<font color="Maroon" title="c14">S2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c15">S3</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E2:33"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="isocat_2.html#E4:33_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="ref" href="isocat_2.html#T15" target="_self" title="ISOCAT_2:th.15">Th15</a></i>;<br/><a NAME="E7:33_1"/><b>then </b>
<font color="Maroon" title="c13">S1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c15">S3</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E5:33_1"><i><font color="Green" title="E42">A13</font></i></a>, <a class="ref" href="nattra_1.html#T25" title="NATTRA_1:th.25">NATTRA_1:25</a></i>;<br/><a NAME="E8:33_1"/><b>then </b><i><font color="Green" title="E44">A15</font></i>: 
<font color="Maroon" title="c13">S1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c15">S3</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/><a NAME="E9:33_1"/><i><font color="Green" title="E45">A16</font></i>: 
<font color="Maroon" title="c13">S1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c14">S2</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E5:33_1"><i><font color="Green" title="E42">A13</font></i></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></i>;<br/><a NAME="E10:33_1"/><i><font color="Green" title="E46">A17</font></i>: 
<font color="Maroon" title="c14">S2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c15">S3</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E6:33_1"><i><font color="Green" title="E43">A14</font></i></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c16">T1</font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c10">s1</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c9">a</font> as    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c13">S1</font>,<font color="Maroon" title="c14">S2</font> <b>by </b><i><a class="txt" href="isocat_2.html#E1:33"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="isocat_2.html#E4:33_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="ref" href="isocat_2.html#T15" target="_self" title="ISOCAT_2:th.15">Th15</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c17">T2</font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c11">s2</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c9">a</font> as    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c14">S2</font>,<font color="Maroon" title="c15">S3</font> <b>by </b><i><a class="txt" href="isocat_2.html#E2:33"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="isocat_2.html#E4:33_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="ref" href="isocat_2.html#T15" target="_self" title="ISOCAT_2:th.15">Th15</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c18">T3</font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2" title="CAT_2:func.2">curry</a> <font color="Maroon" title="c12">s3</font></span>)</span> <a href="cat_2.html#K1" title="CAT_2:func.1">.</a> <font color="Maroon" title="c9">a</font> as    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c13">S1</font>,<font color="Maroon" title="c15">S3</font> <b>by </b><i><a class="txt" href="isocat_2.html#E3:33"><i><font color="Green" title="E32">A3</font></i></a>, <a class="txt" href="isocat_2.html#E4:33_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="ref" href="isocat_2.html#T15" target="_self" title="ISOCAT_2:th.15">Th15</a></i>;<br/><a NAME="E14:33_1"/><i><font color="Green" title="E47">A18</font></i>: 
<span class="p1">(<span class="default"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">S2</font>,<font color="Maroon" title="c15">S3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c17">T2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E2:33"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="isocat_2.html#D5" target="_self" title="ISOCAT_2:def.5">Def5</a></i>;<br/><a NAME="E15:33_1"/><i><font color="Green" title="E48">A19</font></i>: 
<span class="p1">(<span class="default"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c7">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">S1</font>,<font color="Maroon" title="c14">S2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c16">T1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:33"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="isocat_2.html#D5" target="_self" title="ISOCAT_2:def.5">Def5</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c19">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="E1:33_1_1"/><i><font color="Green" title="E49">A20</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">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="c9">a</font>,<font color="Maroon" title="c19">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="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="c9">a</font>,<font color="Maroon" title="c19">b</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#E4:33"><i><font color="Green" title="E33">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="E2:33_1_1"/><i><font color="Green" title="E50">A21</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">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="c9">a</font>,<font color="Maroon" title="c19">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="c6">F3</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="c9">a</font>,<font color="Maroon" title="c19">b</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#E5:33"><i><font color="Green" title="E34">A5</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="E3:33_1_1"/><i><font color="Green" title="E51">A22</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">S1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c19">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c14">S2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c19">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#E9:33_1"><i><font color="Green" title="E45">A16</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="E4:33_1_1"/><i><font color="Green" title="E52">A23</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">S2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c19">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c15">S3</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c19">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#E10:33_1"><i><font color="Green" title="E46">A17</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/><i><font color="Green" title="E53">A24</font></i>: <font color="Maroon" title="c17">T2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font> = 
<font color="Maroon" title="c17">T2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E10:33_1"><i><font color="Green" title="E46">A17</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="c11">s2</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c19">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="c8">t2</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="c9">a</font>,<font color="Maroon" title="c19">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#E5:33"><i><font color="Green" title="E34">A5</font></i></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
;<br/><i><font color="Green" title="E54">A25</font></i>: <font color="Maroon" title="c16">T1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font> = 
<font color="Maroon" title="c16">T1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E9:33_1"><i><font color="Green" title="E45">A16</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="c10">s1</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c19">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="c7">t1</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="c9">a</font>,<font color="Maroon" title="c19">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#E4:33"><i><font color="Green" title="E33">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>thus </b><font color="Maroon" title="c18">T3</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font> = 
<font color="Maroon" title="c18">T3</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E8:33_1"><i><font color="Green" title="E44">A15</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="c12">s3</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c19">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/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span> <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="c9">a</font>,<font color="Maroon" title="c19">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#E6:33"><i><font color="Green" title="E35">A6</font></i></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">t2</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="c9">a</font>,<font color="Maroon" title="c19">b</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="c7">t1</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="c9">a</font>,<font color="Maroon" title="c19">b</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#E1:33"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="isocat_2.html#E2:33"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="nattra_1.html#T27" title="NATTRA_1:th.27">NATTRA_1:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">T2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">T1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:33_1_1"><i><font color="Green" title="E49">A20</font></i></a>, <a class="txt" href="isocat_2.html#E2:33_1_1"><i><font color="Green" title="E50">A21</font></i></a>, <a class="txt" href="isocat_2.html#E5:33_1_1"><i><font color="Green" title="E53">A24</font></i></a>, <a class="txt" href="isocat_2.html#E6:33_1_1"><i><font color="Green" title="E54">A25</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="c17">T2</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</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="c16">T1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:33_1_1"><i><font color="Green" title="E51">A22</font></i></a>, <a class="txt" href="isocat_2.html#E4:33_1_1"><i><font color="Green" title="E52">A23</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="c17">T2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c16">T1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E5:33_1"><i><font color="Green" title="E42">A13</font></i></a>, <a class="txt" href="isocat_2.html#E6:33_1"><i><font color="Green" title="E43">A14</font></i></a>, <a class="ref" href="nattra_1.html#T27" title="NATTRA_1:th.27">NATTRA_1:27</a></i>
;<br/></div><b>end;</b></div><a NAME="E17:33_1"/><b>then </b><i><font color="Green" title="E49">A26</font></i>: 
<font color="Maroon" title="c18">T3</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c17">T2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c16">T1</font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E8:33_1"><i><font color="Green" title="E44">A15</font></i></a>, <a class="ref" href="nattra_1.html#T20" title="NATTRA_1:th.20">NATTRA_1:20</a></i>;<br/><a NAME="E18:33_1"/><i><font color="Green" title="E50">A27</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</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#E8:33"><i><font color="Green" title="E37">A8</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="E19:33_1"/><i><font color="Green" title="E51">A28</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" title="ISOCAT_2:func.5">export</a> <font color="Maroon" title="c6">F3</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c9">a</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#E10:33"><i><font color="Green" title="E39">A10</font></i></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">a</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">S1</font>,<font color="Maroon" title="c15">S3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c18">T3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:33"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="isocat_2.html#D5" target="_self" title="ISOCAT_2:def.5">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">a</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c7">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">a</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E14:33_1"><i><font color="Green" title="E47">A18</font></i></a>, <a class="txt" href="isocat_2.html#E15:33_1"><i><font color="Green" title="E48">A19</font></i></a>, <a class="txt" href="isocat_2.html#E17:33_1"><i><font color="Green" title="E49">A26</font></i></a>, <a class="ref" href="nattra_1.html#T42" title="NATTRA_1:th.42">NATTRA_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">a</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"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c7">t1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">a</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E18:33_1"><i><font color="Green" title="E50">A27</font></i></a>, <a class="txt" href="isocat_2.html#E19:33_1"><i><font color="Green" title="E51">A28</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"><span class="p2">(<span class="default"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p2">(<span class="default"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c7">t1</font></span>)</span></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c9">a</font>
<b>by </b><i><a class="txt" href="isocat_2.html#E7:33"><i><font color="Green" title="E36">A7</font></i></a>, <a class="txt" href="isocat_2.html#E9:33"><i><font color="Green" title="E38">A9</font></i></a>, <a class="ref" href="nattra_1.html#T27" title="NATTRA_1:th.27">NATTRA_1:27</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E13:33"/>
 <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c7">t1</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c8">t2</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <font color="Maroon" title="c7">t1</font></span>)</span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E11:33"><i><font color="Green" title="E40">A11</font></i></a>, <a class="ref" href="nattra_1.html#T20" title="NATTRA_1:th.20">NATTRA_1:20</a></i>;<br/>


</div>
