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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>

















<b>assume </b><a NAME="E1:36"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<a NAME="E2:36"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#T25">NATTRA_1:25</a></i>;<br/>
<a NAME="E3:36"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:36"><i><font color="Green">E28</font></i></a>, <a class="ref" href="isocat_1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E4:36"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#T25">NATTRA_1:25</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><a NAME="E1:36_1"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="isocat_1.html#E1:36"><i><font color="Green">E28</font></i></a>, <a class="ref" href="isocat_1.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E2:36_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K13">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K13">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K13">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="ref" href="cat_1.html#T113">CAT_1:113</a></i>;<br/><a NAME="E3:36_1"/><i><font color="Green">E34</font></i>: 
(  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="txt" href="isocat_1.html#E1:36"><i><font color="Green">E28</font></i></a>, <a class="ref" href="isocat_1.html#T30" target="_self">Th30</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font> = 
<font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E2:36"><i><font color="Green">E29</font></i></a>, <a class="ref" href="isocat_1.html#T28" target="_self">Th28</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E1:36"><i><font color="Green">E28</font></i></a>, <a class="ref" href="nattra_1.html#T27">NATTRA_1:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E3:36_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="nattra_1.html#T13">NATTRA_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="isocat_1.html#E3:36"><i><font color="Green">E30</font></i></a>, <a class="txt" href="isocat_1.html#E1:36_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="isocat_1.html#E2:36_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="nattra_1.html#T27">NATTRA_1:27</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:36"/>
<font color="Maroon">c<sub>7</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="isocat_1.html#E4:36"><i><font color="Green">E31</font></i></a>, <a class="ref" href="isocat_1.html#T31" target="_self">Th31</a></i>;<br/>


</div>
