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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>, <font color="Maroon" title="c4">D</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c5">F1</font>, <font color="Maroon" title="c6">F2</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="c7">G1</font>, <font color="Maroon" title="c8">G2</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="c9">H1</font>, <font color="Maroon" title="c10">H2</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c4">D</font>;<br/><b>let </b><font color="Maroon" title="c11">s</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c5">F1</font>,<font color="Maroon" title="c6">F2</font>;<br/><b>let </b><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>;<br/><b>let </b><font color="Maroon" title="c13">u</font> be    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c9">H1</font>,<font color="Maroon" title="c10">H2</font>;<br/>

























<b>assume </b><b>that </b><br/><a NAME="E1:49"/><i><font color="Green" title="E35">A1</font></i>: 
<font color="Maroon" title="c5">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c6">F2</font>
 <b>and </b><br/><a NAME="E2:49"/><i><font color="Green" title="E36">A2</font></i>: 
<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>
 <b>and </b><br/><a NAME="E3:49"/><i><font color="Green" title="E37">A3</font></i>: 
<font color="Maroon" title="c9">H1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c10">H2</font>
 ;<br/>

<a NAME="E4:49"/><i><font color="Green" title="E38">A4</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c10">H2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c10">H2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>;<br/>
<a NAME="E5:49"/><i><font color="Green" title="E39">A5</font></i>: 
( <font color="Maroon" title="c13">u</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</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">u</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c6">F2</font> &amp; <font color="Maroon" title="c9">H1</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</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="c6">F2</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="c9">H1</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</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="c6">F2</font> &amp; <font color="Maroon" title="c9">H1</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">G1</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">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="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">s</font> )
 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:49"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="isocat_1.html#E2:49"><i><font color="Green" title="E36">A2</font></i></a>, <a class="txt" href="isocat_1.html#E3:49"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="isocat_1.html#T34" target="_self" title="ISOCAT_1:th.34">Th34</a>, <a class="ref" href="isocat_1.html#T35" target="_self" title="ISOCAT_1:th.35">Th35</a>, <a class="ref" href="isocat_1.html#T36" target="_self" title="ISOCAT_1:th.36">Th36</a></i>;<br/>
<a NAME="E6:49"/><i><font color="Green" title="E40">A6</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F1</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="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</font>
 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:49"><i><font color="Green" title="E35">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="E7:49"/><i><font color="Green" title="E41">A7</font></i>: 
<font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <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">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c8">G2</font>
 
<b>by </b><i><a class="txt" href="isocat_1.html#E2:49"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></i>;<br/>
<a NAME="E8:49"/><b>then </b><i><font color="Green" title="E42">A8</font></i>: 
( <font color="Maroon" title="c7">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</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#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</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="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</font> )
 
<b>by </b><i><a class="txt" href="isocat_1.html#E2:49"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></i>;<br/>
<a NAME="E9:49"/><i><font color="Green" title="E43">A9</font></i>: 
<font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <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="c10">H2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c8">G2</font>
 
<b>by </b><i><a class="txt" href="isocat_1.html#E3:49"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></i>;<br/>
<a NAME="E10:49"/><b>then </b><i><font color="Green" title="E44">A10</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</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="c10">H2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</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="E11:49"/>
<font color="Maroon" title="c7">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">G1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</font>
 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:49"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="isocat_1.html#T27" target="_self" title="ISOCAT_1:th.27">Th27</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c13">u</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</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="c11">s</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">u</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">G2</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c6">F2</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="c9">H1</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</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="c6">F2</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="c9">H1</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">G1</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">s</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E8:49"><i><font color="Green" title="E42">A8</font></i></a>, <a class="ref" href="isocat_1.html#T32" target="_self" title="ISOCAT_1:th.32">Th32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c13">u</font> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c8">G2</font></span>)</span> <a href="isocat_1.html#K5" title="ISOCAT_1:func.5">*</a> <font color="Maroon" title="c6">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="c9">H1</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</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="c6">F2</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="c9">H1</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c7">G1</font></span>)</span> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <font color="Maroon" title="c11">s</font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E4:49"><i><font color="Green" title="E38">A4</font></i></a>, <a class="txt" href="isocat_1.html#E5:49"><i><font color="Green" title="E39">A5</font></i></a>, <a class="txt" href="isocat_1.html#E6:49"><i><font color="Green" title="E40">A6</font></i></a>, <a class="txt" href="isocat_1.html#E8:49"><i><font color="Green" title="E42">A8</font></i></a>, <a class="txt" href="isocat_1.html#E10:49"><i><font color="Green" title="E44">A10</font></i></a>, <a class="ref" href="nattra_1.html#T28" title="NATTRA_1:th.28">NATTRA_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">u</font> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c12">t</font></span>)</span> <a href="isocat_1.html#K6" title="ISOCAT_1:func.6">(#)</a> <font color="Maroon" title="c11">s</font>
<b>by </b><i><a class="txt" href="isocat_1.html#E7:49"><i><font color="Green" title="E41">A7</font></i></a>, <a class="txt" href="isocat_1.html#E9:49"><i><font color="Green" title="E43">A9</font></i></a>, <a class="ref" href="isocat_1.html#T33" target="_self" title="ISOCAT_1:th.33">Th33</a></i>
;<br/><br/>


</div>
