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

<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font>, <font color="Olive" title="b3">F3</font> being    <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>  st <font color="Olive" title="b1">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b2">F2</font> &amp; <font color="Olive" title="b2">F2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b3">F3</font> holds <br/> for <font color="Olive" title="b4">t1</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Olive" title="b1">F1</font>,<font color="Olive" title="b2">F2</font><br/>  for <font color="Olive" title="b5">t2</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Olive" title="b2">F2</font>,<font color="Olive" title="b3">F3</font> holds   <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">t2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b4">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="Olive" title="b5">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="Olive" title="b4">t1</font></span>)</span></span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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> &amp; <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> implies  for <font color="Olive" title="b1">t1</font> being    <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/>  for <font color="Olive" title="b2">t2</font> being    <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> holds   <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b1">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="Olive" title="b2">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="Olive" title="b1">t1</font></span>)</span> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:32"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:32"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t1</font> being    <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/>  for <font color="Olive" title="b2">t2</font> being    <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> holds   <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b1">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="Olive" title="b2">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="Olive" title="b1">t1</font></span>)</span></span><br/>

<a NAME="E3:32"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/>
<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t2</font> being    <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> holds   <a href="isocat_2.html#K6" title="ISOCAT_2:func.6">export</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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="Olive" title="b1">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></span><br/><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <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></span><br/>



<a NAME="E4:32"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/>
<a NAME="E5:32"/><span class="lab"><font color="Green" title="E33">A5</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="isocat_2.html#T23" target="_self" title="ISOCAT_2:th.23">Th27</a></span>;<br/>
<a NAME="E6:32"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A6</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/>
<a NAME="E7:32"/><span class="lab"><font color="Green" title="E35">A7</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="isocat_2.html#T23" target="_self" title="ISOCAT_2:th.23">Th27</a></span>;<br/>
<a NAME="E8:32"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A8</font></span>: 
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/>
<a NAME="E9:32"/><span class="lab"><font color="Green" title="E37">A9</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="nattra_1.html#T23" title="NATTRA_1:th.23">NATTRA_1:23</a></span>;<br/>
<a NAME="E10:32"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A10</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="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></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c10">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#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c11">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#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c9">a</font>, <font color="Maroon" title="c12">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#K9" title="CAT_1:func.9">.</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T7" target="_self" title="ISOCAT_2:th.7">Th8</a></span>;<br/><a NAME="E2:32_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T23" title="CAT_2:th.23">CAT_2:23</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">s1</font> = <font color="Maroon" title="c7">t1</font>, <font color="Maroon" title="c14">s2</font> = <font color="Maroon" title="c8">t2</font>, <font color="Maroon" title="c15">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="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C</font> ;<br/><a NAME="E4:32_1"/><span class="lab"><font color="Green" title="E39">A11</font></span>: 
<font color="Maroon" title="c11">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T20" target="_self" title="ISOCAT_2:th.20">Th24</a></span>;<br/><a NAME="E5:32_1"/><span class="lab"><font color="Green" title="E40">A12</font></span>: 
<font color="Maroon" title="c12">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T20" target="_self" title="ISOCAT_2:th.20">Th24</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">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="c14">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="c11">S2</font>,<font color="Maroon" title="c12">S3</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E4:32_1"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="ref" href="isocat_2.html#T13" target="_self" title="ISOCAT_2:th.13">Th15</a></span>;<br/><a NAME="E7:32_1"/><span class="lab"><font color="Green" title="E41">A13</font></span>: 
<font color="Maroon" title="c11">S2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c12">S3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E4:32_1"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="txt" href="#E5:32_1"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <a class="ref" href="isocat_2.html#T13" target="_self" title="ISOCAT_2:th.13">Th15</a></span>;<br/><a NAME="E8:32_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A14</font></span>: 
<font color="Maroon" title="c11">S2</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c12">S3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/><a NAME="E9:32_1"/><span class="lab"><font color="Green" title="E43">A15</font></span>: 
<font color="Maroon" title="c10">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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_2.html#T20" target="_self" title="ISOCAT_2:th.20">Th24</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">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="c13">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="c10">S1</font>,<font color="Maroon" title="c11">S2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E4:32_1"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="ref" href="isocat_2.html#T13" target="_self" title="ISOCAT_2:th.13">Th15</a></span>;<br/><a NAME="E11:32_1"/><span class="lab"><font color="Green" title="E44">A16</font></span>: 
( <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="c11">S2</font>,<font color="Maroon" title="c12">S3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c16">T2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <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="c10">S1</font>,<font color="Maroon" title="c11">S2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c17">T1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="isocat_2.html#D5" target="_self" title="ISOCAT_2:def.5">Def5</a></span>;<br/><a NAME="E12:32_1"/><span class="lab"><font color="Green" title="E45">A17</font></span>: 
<font color="Maroon" title="c10">S1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c11">S2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E9:32_1"><span class="lab"><font color="Green" title="E43">A15</font></span></a>, <a class="txt" href="#E4:32_1"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="ref" href="isocat_2.html#T13" target="_self" title="ISOCAT_2:th.13">Th15</a></span>;<br/><a NAME="E13:32_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">S1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c12">S3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:32_1"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="ref" href="nattra_1.html#T23" title="NATTRA_1:th.23">NATTRA_1:23</a></span>;<br/><a NAME="E14:32_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A18</font></span>: 
<font color="Maroon" title="c10">S1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c12">S3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/><span class="kw">reconsider </span><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="c15">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="c10">S1</font>,<font color="Maroon" title="c12">S3</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:32"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="txt" href="#E9:32_1"><span class="lab"><font color="Green" title="E43">A15</font></span></a>, <a class="txt" href="#E5:32_1"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <a class="ref" href="isocat_2.html#T13" target="_self" title="ISOCAT_2:th.13">Th15</a></span>;<br/><a NAME="E16:32_1"/><span class="lab"><font color="Green" title="E47">A19</font></span>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">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#K9" title="CAT_1:func.9">.</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#K9" title="CAT_1:func.9">.</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>  &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">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#K9" title="CAT_1:func.9">.</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#K9" title="CAT_1:func.9">.</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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:32"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E8:32"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/><a NAME="E17:32_1"/><span class="lab"><font color="Green" title="E48">A20</font></span>: 
<font color="Maroon" title="c10">S1</font> <a href="nattra_1.html#R1" title="NATTRA_1:pred.1">is_transformable_to</a> <font color="Maroon" title="c11">S2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:32_1"><span class="lab"><font color="Green" title="E45">A17</font></span></a>, <a class="ref" href="nattra_1.html#D7" title="NATTRA_1:def.7">NATTRA_1:def 7</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">T2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c17">T1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font></span><br/><a NAME="E1:32_1_1"/><span class="lab"><font color="Green" title="E49">A21</font></span>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c4">F1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</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#K9" title="CAT_1:func.9">.</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>  &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">F2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</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#K9" title="CAT_1:func.9">.</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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:32"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E3:32"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/><a NAME="E2:32_1_1"/><span class="lab"><font color="Green" title="E50">A22</font></span>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c10">S1</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c19">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">S2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</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>  &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">S2</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c19">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c12">S3</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:32_1"><span class="lab"><font color="Green" title="E48">A20</font></span></a>, <a class="txt" href="#E8:32_1"><span class="lab"><font color="Green" title="E42">A14</font></span></a>, <a class="ref" href="nattra_1.html#D2" title="NATTRA_1:def.2">NATTRA_1:def 2</a></span>;<br/><span class="lab"><font color="Green" title="E51">A23</font></span>: <font color="Maroon" title="c17">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="c17">T1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:32_1"><span class="lab"><font color="Green" title="E48">A20</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c13">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>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:32"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
;<br/><span class="lab"><font color="Green" title="E52">A24</font></span>: <font color="Maroon" title="c16">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="c16">T2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:32_1"><span class="lab"><font color="Green" title="E42">A14</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c14">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>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:32"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
;<br/><span class="kw">thus </span><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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:32_1"><span class="lab"><font color="Green" title="E46">A18</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c15">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>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T3" title="CAT_2:th.3">CAT_2:3</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:32"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="ref" href="nattra_1.html#D5" title="NATTRA_1:def.5">NATTRA_1:def 5</a></span>
<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#K5" title="CAT_1:func.5">*</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="nattra_1.html#T25" title="NATTRA_1:th.25">NATTRA_1:25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">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#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">T1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32_1_1"><span class="lab"><font color="Green" title="E49">A21</font></span></a>, <a class="txt" href="#E4:32_1_1"><span class="lab"><font color="Green" title="E52">A24</font></span></a>, <a class="txt" href="#E3:32_1_1"><span class="lab"><font color="Green" title="E51">A23</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">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="c17">T1</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32_1_1"><span class="lab"><font color="Green" title="E50">A22</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">T2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c17">T1</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c19">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:32_1"><span class="lab"><font color="Green" title="E45">A17</font></span></a>, <a class="txt" href="#E7:32_1"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="ref" href="nattra_1.html#T25" title="NATTRA_1:th.25">NATTRA_1:25</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E19:32_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A25</font></span>: 
<font color="Maroon" title="c18">T3</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c16">T2</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c17">T1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:32_1"><span class="lab"><font color="Green" title="E46">A18</font></span></a>, <a class="ref" href="nattra_1.html#T19" title="NATTRA_1:th.19">NATTRA_1:19</a></span>;<br/><span class="kw">thus </span><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="c10">S1</font>,<font color="Maroon" title="c12">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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:32"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="isocat_2.html#D5" target="_self" title="ISOCAT_2:def.5">Def5</a></span>
<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#K1" title="CAT_1:func.1">*</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:32_1"><span class="lab"><font color="Green" title="E44">A16</font></span></a>, <a class="txt" href="#E19:32_1"><span class="lab"><font color="Green" title="E49">A25</font></span></a>, <a class="ref" href="nattra_1.html#T36" title="NATTRA_1:th.36">NATTRA_1:36</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:32_1"><span class="lab"><font color="Green" title="E47">A19</font></span></a>, <a class="ref" href="cat_1.html#D10" title="CAT_1:def.10">CAT_1:def 10</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:32"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E7:32"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="ref" href="nattra_1.html#T25" title="NATTRA_1:th.25">NATTRA_1:25</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E12:32"/>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:32"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E8:32"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="ref" href="nattra_1.html#T18" title="NATTRA_1:th.18">NATTRA_1:18</a>, <a class="ref" href="nattra_1.html#T19" title="NATTRA_1:th.19">NATTRA_1:19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
