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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">D</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c5">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="c3">B</font>;<br/><b>let </b><font color="Maroon" title="c6">G1</font>, <font color="Maroon" title="c7">G2</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">B</font>,<font color="Maroon" title="c4">C</font>;<br/><b>let </b><font color="Maroon" title="c8">H</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c4">C</font>,<font color="Maroon" title="c2">D</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">G1</font>,<font color="Maroon" title="c7">G2</font>;<br/>

















<b>assume </b><a NAME="E1:39"/><i><font color="Green" title="E31">A1</font></i>: 
<font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G2</font>
 ;<br/>

<a NAME="E2:39"/><b>then </b><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c8">H</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">G1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c8">H</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G2</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="E3:39"/><b>then </b><i><font color="Green" title="E33">A3</font></i>: 
( <font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">G1</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G2</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font> )
 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:39"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></i>;<br/>
<a NAME="E4:39"/><i><font color="Green" title="E34">A4</font></i>: 
( <font color="Maroon" title="c8">H</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</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="c8">H</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">G1</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font> &amp; <font color="Maroon" title="c8">H</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</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="c8">H</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G2</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">v</font> = <font color="Maroon" title="c8">H</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</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="c5">F</font></span>)</span> as    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">G1</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G2</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c11">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="E1:39_1"/><i><font color="Green" title="E35">A5</font></i>: 
( <font color="Maroon" title="c6">G1</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">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">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">a</font> &amp; <font color="Maroon" title="c7">G2</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">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">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">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="c8">H</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c5">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c9">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="c5">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">a</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E2:39"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="isocat_1.html#T29" target="_self" title="ISOCAT_1:th.29">Th29</a></i>
<br/>.= 
<font color="Maroon" title="c8">H</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <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="c5">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c11">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E1:39"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="isocat_1.html#T28" target="_self" title="ISOCAT_1:th.28">Th28</a></i>
<br/>.= 
<font color="Maroon" title="c8">H</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <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="c5">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E1:39"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="isocat_1.html#E1:39_1"><i><font color="Green" title="E35">A5</font></i></a>, <a class="ref" href="isocat_1.html#T29" target="_self" title="ISOCAT_1:th.29">Th29</a></i>
<br/>.= 
<font color="Maroon" title="c10">v</font> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c11">a</font>
<b>by </b><i><a class="txt" href="isocat_1.html#E3:39"><i><font color="Green" title="E33">A3</font></i></a>, <a class="txt" href="isocat_1.html#E4:39"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="isocat_1.html#T28" target="_self" title="ISOCAT_1:th.28">Th28</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:39"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">H</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c5">F</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">H</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</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="c5">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="isocat_1.html#E3:39"><i><font color="Green" title="E33">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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