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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/>



<b>assume </b><a NAME="E1:72"/><i><font color="Green" title="E56">A1</font></i>: 
<font color="Maroon" title="c1">A</font> is <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">NATTRA_1:def 19</a><br/>

<a NAME="E2:72"/>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span>
 
;<br/>
<a NAME="E3:72"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nattra_1.html#K11" title="NATTRA_1:func.11">NatTrans</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D18" target="_self" title="NATTRA_1:def.18">Def18</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">F1</font>, <font color="Maroon" title="c5">F2</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="c1">A</font>, <font color="Maroon" title="c6">t</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><b> such that </b><br/><a NAME="E5:72"/><i><font color="Green" title="E57">A2</font></i>: 
( <font color="Maroon" title="c3">f</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="c4">F1</font>,<font color="Maroon" title="c5">F2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c6">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <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> )
 <b>by </b><i><a class="ref" href="nattra_1.html#D16" target="_self" title="NATTRA_1:def.16">Def16</a></i>;<br/>
<a NAME="E6:72"/>
<font color="Maroon" title="c4">F1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_2.html#K7" title="CAT_2:func.7">Funct</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="cat_2.html#D2" title="CAT_2:def.2">CAT_2:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">a</font> = <font color="Maroon" title="c4">F1</font> as   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span> <b>by </b><i><a class="ref" href="nattra_1.html#D18" target="_self" title="NATTRA_1:def.18">Def18</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c7">a</font>
;<br/>

<a NAME="E8:72"/>
<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>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E5:72"><i><font color="Green" title="E57">A2</font></i></a>, <a class="ref" href="nattra_1.html#D7" target="_self" title="NATTRA_1:def.7">Def7</a></i>;<br/>
<a NAME="E9:72"/><b>then </b><i><font color="Green" title="E58">A3</font></i>: 
<font color="Maroon" title="c4">F1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">F2</font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:72"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="nattra_1.html#T49" target="_self" title="NATTRA_1:th.49">Th49</a></i>;<br/>
<a NAME="E10:72"/><b>then </b>
<font color="Maroon" title="c6">t</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <font color="Maroon" title="c4">F1</font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:72"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="nattra_1.html#T50" target="_self" title="NATTRA_1:th.50">Th50</a></i>;<br/>
<b>hence </b><a NAME="E11:72"/>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c7">a</font>
 <b>by </b><i><a class="txt" href="nattra_1.html#E5:72"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="nattra_1.html#E9:72"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="nattra_1.html#D18" target="_self" title="NATTRA_1:def.18">Def18</a></i>;<br/>


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