<?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="Red">::  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 <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><br/> for <font color="Olive" title="b4">G1</font>, <font color="Olive" title="b5">G2</font>, <font color="Olive" title="b6">G3</font> being   <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><br/> for <font color="Olive" title="b7">s</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="b8">s9</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><br/> for <font color="Olive" title="b9">t</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Olive" title="b4">G1</font>,<font color="Olive" title="b5">G2</font><br/> for <font color="Olive" title="b10">t9</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Olive" title="b5">G2</font>,<font color="Olive" title="b6">G3</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> &amp; <font color="Olive" title="b4">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b5">G2</font> &amp; <font color="Olive" title="b5">G2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b6">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b10">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b9">t</font></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b8">s9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b7">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b10">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Olive" title="b8">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b9">t</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Olive" title="b7">s</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 <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G3</font> being   <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><br/> for <font color="Olive" title="b4">s</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="b5">s9</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><br/> for <font color="Olive" title="b6">t</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font><br/> for <font color="Olive" title="b7">t9</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font>  st <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> &amp; <font color="Olive" title="b1">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b2">G2</font> &amp; <font color="Olive" title="b2">G2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Olive" title="b3">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b7">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b6">t</font></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">s9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b4">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Olive" title="b5">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">t</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Olive" title="b4">s</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">G1</font>, <font color="Maroon" title="c8">G2</font>, <font color="Maroon" title="c9">G3</font> be    <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</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">s9</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><br/> for <font color="Olive" title="b3">t</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c7">G1</font>,<font color="Maroon" title="c8">G2</font><br/> for <font color="Olive" title="b4">t9</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c8">G2</font>,<font color="Maroon" title="c9">G3</font>  st <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> &amp; <font color="Maroon" title="c7">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b4">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b3">t</font></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">s9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Olive" title="b2">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">t</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Olive" title="b1">s</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c10">s</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s9</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><br/> for <font color="Olive" title="b2">t</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c7">G1</font>,<font color="Maroon" title="c8">G2</font><br/> for <font color="Olive" title="b3">t9</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c8">G2</font>,<font color="Maroon" title="c9">G3</font>  st <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> &amp; <font color="Maroon" title="c7">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b2">t</font></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">s9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Olive" title="b1">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c10">s</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c11">s9</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">t</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c7">G1</font>,<font color="Maroon" title="c8">G2</font><br/> for <font color="Olive" title="b2">t9</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c8">G2</font>,<font color="Maroon" title="c9">G3</font>  st <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> &amp; <font color="Maroon" title="c7">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c10">s</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c12">t</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c7">G1</font>,<font color="Maroon" title="c8">G2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">t9</font> being   <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c8">G2</font>,<font color="Maroon" title="c9">G3</font>  st <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> &amp; <font color="Maroon" title="c7">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c10">s</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c13">t9</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c8">G2</font>,<font color="Maroon" title="c9">G3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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> &amp; <font color="Maroon" title="c7">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font> &amp; <font color="Maroon" title="c8">G2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c10">s</font></span>)</span> )</span><br/>

























<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:56"/><span class="lab"><font color="Green" title="E35">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="E2:56"/><span class="lab"><font color="Green" title="E36">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>
 <span class="kw">and </span><br/><a NAME="E3:56"/><span class="lab"><font color="Green" title="E37">A3</font></span>: 
<font color="Maroon" title="c7">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">G2</font>
 <span class="kw">and </span><br/><a NAME="E4:56"/><span class="lab"><font color="Green" title="E38">A4</font></span>: 
<font color="Maroon" title="c8">G2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c10">s</font></span>)</span></span><br/>

<a NAME="E5:56"/><span class="lab"><font color="Green" title="E39">A5</font></span>: 
( <font color="Maroon" title="c13">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c11">s9</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> &amp; <font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c10">s</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="isocat_1.html#T41" target="_self" title="ISOCAT_1:th.41">Th41</a></span>;<br/>
<a NAME="E6:56"/><span class="lab"><font color="Green" title="E40">A6</font></span>: 
<font color="Maroon" title="c7">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <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="c8">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></span>;<br/>
<a NAME="E7:56"/><span class="lab"><font color="Green" title="E41">A7</font></span>: 
<font color="Maroon" title="c8">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <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="c8">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></span>;<br/>
<a NAME="E8:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A8</font></span>: 
<font color="Maroon" title="c7">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <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="c8">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:56"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="ref" href="nattra_1.html#T25" title="NATTRA_1:th.25">NATTRA_1:25</a></span>;<br/>
<a NAME="E9:56"/><span class="lab"><font color="Green" title="E43">A9</font></span>: 
<font color="Maroon" title="c8">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <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="c9">G3</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></span>;<br/>
<a NAME="E10:56"/><span class="lab"><font color="Green" title="E44">A10</font></span>: 
<font color="Maroon" title="c7">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c9">G3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="nattra_1.html#T25" title="NATTRA_1:th.25">NATTRA_1:25</a></span>;<br/>
<a NAME="E11:56"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A11</font></span>: 
<font color="Maroon" title="c7">G1</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <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="c9">G3</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></span>;<br/>
<a NAME="E12:56"/><span class="lab"><font color="Green" title="E46">A12</font></span>: 
<font color="Maroon" title="c9">G3</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <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="c9">G3</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c5">F2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></span>;<br/>
<a NAME="E13:56"/><span class="lab"><font color="Green" title="E47">A13</font></span>: 
<font color="Maroon" title="c8">G2</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <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="c9">G3</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></span>;<br/>
<a NAME="E14:56"/><span class="lab"><font color="Green" title="E48">A14</font></span>: 
<font color="Maroon" title="c9">G3</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <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="c9">G3</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c6">F3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></span>;<br/>
<a NAME="E15:56"/>
<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="#E1:56"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E36">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="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">s9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">s9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c10">s</font></span>)</span></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:56"><span class="lab"><font color="Green" title="E44">A10</font></span></a>, <a class="ref" href="isocat_1.html#T41" target="_self" title="ISOCAT_1:th.41">Th41</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c10">s</font></span>)</span></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E36">A2</font></span></a>, <a class="ref" href="isocat_1.html#T32" target="_self" title="ISOCAT_1:th.32">Th32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c10">s</font></span>)</span></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56"><span class="lab"><font color="Green" title="E37">A3</font></span></a>, <a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="isocat_1.html#T33" target="_self" title="ISOCAT_1:th.33">Th33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:56"><span class="lab"><font color="Green" title="E48">A14</font></span></a>, <a class="txt" href="#E12:56"><span class="lab"><font color="Green" title="E46">A12</font></span></a>, <a class="txt" href="#E11:56"><span class="lab"><font color="Green" title="E45">A11</font></span></a>, <a class="ref" href="nattra_1.html#T28" title="NATTRA_1:th.28">NATTRA_1:28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:56"><span class="lab"><font color="Green" title="E46">A12</font></span></a>, <a class="txt" href="#E6:56"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="txt" href="#E13:56"><span class="lab"><font color="Green" title="E47">A13</font></span></a>, <a class="ref" href="nattra_1.html#T28" title="NATTRA_1:th.28">NATTRA_1:28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="txt" href="#E4:56"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="isocat_1.html#T41" target="_self" title="ISOCAT_1:th.41">Th41</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">G3</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c5">F2</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p3">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:56"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="txt" href="#E9:56"><span class="lab"><font color="Green" title="E43">A9</font></span></a>, <a class="txt" href="#E7:56"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="ref" href="nattra_1.html#T28" title="NATTRA_1:th.28">NATTRA_1:28</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">t9</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c11">s9</font></span>)</span> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">t</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c10">s</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:56"><span class="lab"><font color="Green" title="E48">A14</font></span></a>, <a class="txt" href="#E9:56"><span class="lab"><font color="Green" title="E43">A9</font></span></a>, <a class="txt" href="#E8:56"><span class="lab"><font color="Green" title="E42">A8</font></span></a>, <a class="txt" href="#E5:56"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="ref" href="nattra_1.html#T28" title="NATTRA_1:th.28">NATTRA_1:28</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
