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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>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <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="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c5">f</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>;<br/>







<b>assume </b><a NAME="E1:60"/><i><font color="Green" title="E49">A1</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<a NAME="E2:60"/>
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</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="c1">A</font>,<font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nattra_1.html#K11" title="NATTRA_1:func.11">NatTrans</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</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="c6">F1</font>, <font color="Maroon" title="c7">F2</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>, <font color="Maroon" title="c8">t</font> being    <a href="nattra_1.html#M2" title="NATTRA_1:mode.2">natural_transformation</a> of <font color="Maroon" title="c6">F1</font>,<font color="Maroon" title="c7">F2</font><b> such that </b><br/><a NAME="E4:60"/><i><font color="Green" title="E50">A2</font></i>: 
( <font color="Maroon" title="c5">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="c6">F1</font>,<font color="Maroon" title="c7">F2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c8">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c6">F1</font> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <font color="Maroon" title="c7">F2</font> )
 <b>by </b><i><a class="ref" href="nattra_1.html#D15" target="_self" title="NATTRA_1:def.15">Def15</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">F1</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c7">F2</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c8">t</font>
;<br/>

<b>thus </b><font color="Maroon" title="c3">a</font> = 
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">f</font>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:60"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c6">F1</font>
<b>by </b><i><a class="txt" href="nattra_1.html#E4:60"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="nattra_1.html#T39" target="_self" title="NATTRA_1:th.39">Th39</a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c4">b</font> = 
 <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">f</font>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:60"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="cat_1.html#T23" title="CAT_1:th.23">CAT_1:23</a></i>
<br/>.= 
<font color="Maroon" title="c7">F2</font>
<b>by </b><i><a class="txt" href="nattra_1.html#E4:60"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="nattra_1.html#T39" target="_self" title="NATTRA_1:th.39">Th39</a></i>
;<br/>

<b>thus </b><a NAME="E7:60"/>
<font color="Maroon" title="c5">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="c6">F1</font>,<font color="Maroon" title="c7">F2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c8">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="nattra_1.html#E4:60"><i><font color="Green" title="E50">A2</font></i></a></i>;<br/>


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