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<div class="add">

<a NAME="E1:56_1_1"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="functor2.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="functor2.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="functor3.html#E1:56"><i><font color="Green">E31</font></i></a>, <a class="ref" href="functor3.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E2:56_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="functor2.html#R1">is_transformable_to</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="functor3.html#E1:56"><i><font color="Green">E31</font></i></a>, <a class="ref" href="functor3.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E3:56_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>5</sub></font> <a href="functor2.html#K2">!</a> <font color="Olive">b<sub>1</sub></font> is <a href="altcat_3.html#V3">iso</a>
 
<b>by </b><i><a class="txt" href="functor3.html#E1:56"><i><font color="Green">E31</font></i></a>, <a class="ref" href="functor3.html#D5" target="_self">Def5</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="functor2.html#M2">natural_transformation</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E5:56_1_1"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor2.html#K2">!</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="altcat_3.html#K1">"</a>  &amp; <font color="Maroon">c<sub>6</sub></font> <a href="functor2.html#K2">!</a> <font color="Olive">b<sub>1</sub></font> is <a href="altcat_3.html#V3">iso</a> )
 <b>by </b><i><a class="txt" href="functor3.html#E1:56_1_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="functor3.html#E2:56_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="functor3.html#T32" target="_self">Th32</a></i>;<br/>
<a NAME="E6:56_1_1"/>
<font color="Maroon">c<sub>6</sub></font> is    <a href="functor3.html#M1" target="_self">natural_equivalence</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:56_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="functor3.html#R1" target="_self">are_naturally_equivalent</a> 
 <b>by </b><i><a class="txt" href="functor3.html#E1:56"><i><font color="Green">E31</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="functor3.html#D5" target="_self">FUNCTOR3:def 5</a><br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>thus </b><a NAME="E2:56_1_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="functor2.html#K2">!</a> <font color="Maroon">c<sub>7</sub></font> is <a href="altcat_3.html#V3">iso</a>
 <b>by </b><i><a class="txt" href="functor3.html#E5:56_1_1"><i><font color="Green">E34</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="functor3.html#M1" target="_self">natural_equivalence</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>thus </b><a NAME="E8:56_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor2.html#K2">!</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="altcat_3.html#K1">"</a> 
 <b>by </b><i><a class="txt" href="functor3.html#E5:56_1_1"><i><font color="Green">E34</font></i></a></i>;<br/>


</div>
