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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">F</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>;<br/><b>let </b><font color="Maroon" title="c5">G1</font>, <font color="Maroon" title="c6">G2</font>, <font color="Maroon" title="c7">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>;<br/><b>let </b><font color="Maroon" title="c8">t</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c6">G2</font>;<br/><b>let </b><font color="Maroon" title="c9">t'</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">G2</font>,<font color="Maroon" title="c7">G3</font>;<br/>

















<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E27">A1</font></i>: 
( <font color="Maroon" title="c5">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">G2</font> &amp; <font color="Maroon" title="c6">G2</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G3</font> )
 ;<br/>

<a NAME="E2:37"/><b>then </b><i><font color="Green" title="E28">A2</font></i>: 
( <font color="Maroon" title="c5">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</font> &amp; <font color="Maroon" title="c6">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G3</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</font> )
 
<b>by </b><i><a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></i>;<br/>
<a NAME="E3:37"/><b>then </b><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c5">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G3</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#T25" title="NATTRA_1:th.25">NATTRA_1:25</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">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="E1:37_1"/><i><font color="Green" title="E30">A4</font></i>: 
( <font color="Maroon" title="c9">t'</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t'</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font> &amp; <font color="Maroon" title="c8">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">t</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font> )
 <b>by </b><i><a class="txt" href="isocat_1.html#E1:37"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="isocat_1.html#T29" target="_self" title="ISOCAT_1:th.29">Th29</a></i>;<br/><a NAME="E2:37_1"/><i><font color="Green" title="E31">A5</font></i>: 
( <font color="Maroon" title="c5">G1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font> &amp; <font color="Maroon" title="c6">G2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font> &amp; <font color="Maroon" title="c7">G3</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G3</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font> )
 <b>by </b><i><a class="ref" href="cat_1.html#T113" title="CAT_1:th.113">CAT_1:113</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">t'</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t'</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E1:37"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="isocat_1.html#T29" target="_self" title="ISOCAT_1:th.29">Th29</a>, <a class="ref" href="nattra_1.html#T25" title="NATTRA_1:th.25">NATTRA_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t'</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</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="c8">t</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c10">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E1:37"><i><font color="Green" title="E27">A1</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"><span class="p2">(<span class="default"><font color="Maroon" title="c9">t'</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F</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="c8">t</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c10">a</font>
<b>by </b><i><a class="txt" href="isocat_1.html#E2:37"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="isocat_1.html#E1:37_1"><i><font color="Green" title="E30">A4</font></i></a>, <a class="txt" href="isocat_1.html#E2:37_1"><i><font color="Green" title="E31">A5</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="E5:37"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">t'</font> <a href="nattra_1.html#K8" title="NATTRA_1:func.8">`*`</a> <font color="Maroon" title="c8">t</font></span>)</span> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t'</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F</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="c8">t</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c4">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="isocat_1.html#E3:37"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="isocat_1.html#T31" target="_self" title="ISOCAT_1:th.31">Th31</a></i>;<br/>


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