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<a NAME="E1:38_1_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">F</font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F1</font> &amp; <font color="Maroon">F1</font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F2</font> )
 
<b>by </b><i>, , <a class="txt" href="nattra_1.html#E2:38_1_1"><i><font color="Green">E26</font></i></a></i>;<br/>
<a NAME="E2:38_1_1"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>  st  <a href="cat_1.html#K6">Hom</a> <font color="Olive">a</font>,<font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">f</font> being   <a href="cat_1.html#M1">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font> holds  <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Olive">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Olive">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Olive">f</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Olive">a</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:38_1_1"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>  st  <a href="cat_1.html#K6">Hom</a> <font color="Olive">a</font>,<font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">f</font> being   <a href="cat_1.html#M1">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font> holds  <span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Olive">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Olive">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Olive">f</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Olive">a</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:38_1_1"/>
<font color="Maroon">t2</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t1</font> is    <a href="nattra_1.html#M2" target="_self">natural_transformation</a> of <font color="Maroon">F</font>,<font color="Maroon">F2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:38_1_1_1"/>
<font color="Maroon">F</font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">F2</font>
 <b>by </b><i>, , </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D8" target="_self">NATTRA_1:def 8</a><br/>

<b>thus </b><a NAME="E2:38_1_1_1"/>
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>  st  <a href="cat_1.html#K6">Hom</a> <font color="Olive">a</font>,<font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">f</font> being   <a href="cat_1.html#M1">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Olive">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Olive">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Olive">f</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Olive">a</font></span>)</span>
 <b>by </b><i>, , , <a class="txt" href="nattra_1.html#E3:38_1_1"><i><font color="Green">E27</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:38_1_1"/>
<font color="Maroon">t2</font> <a href="nattra_1.html#K6" target="_self">`*`</a> <font color="Maroon">t1</font> is    <a href="nattra_1.html#M2" target="_self">natural_transformation</a> of <font color="Maroon">F</font>,<font color="Maroon">F2</font>
 ;<br/>


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