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<b>let </b><font color="Maroon">S</font> be    <a href="nattra_1.html#M4" target="_self">NatTrans-DOMAIN</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">T</font> be    <a href="nattra_1.html#M4" target="_self">NatTrans-DOMAIN</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:57_1_2"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> iff  ex <font color="Olive">F1</font>, <font color="Olive">F2</font> being   <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font> ex <font color="Olive">t</font> being   <a href="nattra_1.html#M2" target="_self">natural_transformation</a> of <font color="Olive">F1</font>,<font color="Olive">F2</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">F1</font>,<font color="Olive">F2</font></span><a href="tarski.html#K4">]</a></span>,<font color="Olive">t</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Olive">F1</font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Olive">F2</font> ) )
 <b>and </b><br/><a NAME="E2:57_1_2"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> iff  ex <font color="Olive">F1</font>, <font color="Olive">F2</font> being   <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font> ex <font color="Olive">t</font> being   <a href="nattra_1.html#M2" target="_self">natural_transformation</a> of <font color="Olive">F1</font>,<font color="Olive">F2</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">F1</font>,<font color="Olive">F2</font></span><a href="tarski.html#K4">]</a></span>,<font color="Olive">t</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Olive">F1</font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Olive">F2</font> ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:57_1_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> iff  ex <font color="Olive">F1</font>, <font color="Olive">F2</font> being   <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font> ex <font color="Olive">t</font> being   <a href="nattra_1.html#M2" target="_self">natural_transformation</a> of <font color="Olive">F1</font>,<font color="Olive">F2</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">F1</font>,<font color="Olive">F2</font></span><a href="tarski.html#K4">]</a></span>,<font color="Olive">t</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Olive">F1</font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Olive">F2</font> ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:57_1_2_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> iff <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:57_1_2"/>
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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