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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>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</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>10</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>11</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>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>13</sub></font> be    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/>

























<b>assume </b><b>that </b><br/><a NAME="E1:52"/><i><font color="Green">E37</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>
 <b>and </b><br/><a NAME="E2:52"/><i><font color="Green">E38</font></i>: 
<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>
 <b>and </b><br/><a NAME="E3:52"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>8</sub></font>
 <b>and </b><br/><a NAME="E4:52"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<a NAME="E5:52"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">c<sub>9</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>9</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>9</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>9</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:52"><i><font color="Green">E37</font></i></a>, <a class="txt" href="isocat_1.html#E2:52"><i><font color="Green">E38</font></i></a>, <a class="ref" href="isocat_1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E6:52"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="isocat_1.html#E3:52"><i><font color="Green">E39</font></i></a>, <a class="txt" href="isocat_1.html#E4:52"><i><font color="Green">E40</font></i></a>, <a class="ref" href="nattra_1.html#T25">NATTRA_1:25</a></i>;<br/>
<a NAME="E7:52"/><i><font color="Green">E43</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="txt" href="isocat_1.html#E1:52"><i><font color="Green">E37</font></i></a>, <a class="txt" href="isocat_1.html#E2:52"><i><font color="Green">E38</font></i></a>, <a class="ref" href="nattra_1.html#T25">NATTRA_1:25</a></i>;<br/>
<a NAME="E8:52"/><i><font color="Green">E44</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>9</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>4</sub></font> &amp; <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>8</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>8</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>9</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="isocat_1.html#E3:52"><i><font color="Green">E39</font></i></a>, <a class="txt" href="isocat_1.html#E4:52"><i><font color="Green">E40</font></i></a>, <a class="txt" href="isocat_1.html#E6:52"><i><font color="Green">E42</font></i></a>, <a class="ref" href="isocat_1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E9:52"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>8</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>9</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="isocat_1.html#E4:52"><i><font color="Green">E40</font></i></a>, <a class="ref" href="isocat_1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E10:52"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>8</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>8</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:52"><i><font color="Green">E37</font></i></a>, <a class="ref" href="isocat_1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E11:52"/><b>then </b><i><font color="Green">E47</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>8</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="isocat_1.html#E8:52"><i><font color="Green">E44</font></i></a>, <a class="ref" href="nattra_1.html#T25">NATTRA_1:25</a></i>;<br/>
<a NAME="E12:52"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="isocat_1.html#K6" target="_self">(#)</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="isocat_1.html#K6" target="_self">(#)</a> <font color="Maroon">c<sub>10</sub></font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:52"><i><font color="Green">E37</font></i></a>, <a class="txt" href="isocat_1.html#E2:52"><i><font color="Green">E38</font></i></a>, <a class="txt" href="isocat_1.html#E3:52"><i><font color="Green">E39</font></i></a>, <a class="txt" href="isocat_1.html#E4:52"><i><font color="Green">E40</font></i></a>, <a class="ref" href="isocat_1.html#T41" target="_self">Th41</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="isocat_1.html#K6" target="_self">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E6:52"><i><font color="Green">E42</font></i></a>, <a class="txt" href="isocat_1.html#E7:52"><i><font color="Green">E43</font></i></a>, <a class="ref" href="isocat_1.html#T41" target="_self">Th41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E1:52"><i><font color="Green">E37</font></i></a>, <a class="txt" href="isocat_1.html#E2:52"><i><font color="Green">E38</font></i></a>, <a class="ref" href="isocat_1.html#T32" target="_self">Th32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E3:52"><i><font color="Green">E39</font></i></a>, <a class="txt" href="isocat_1.html#E4:52"><i><font color="Green">E40</font></i></a>, <a class="ref" href="isocat_1.html#T33" target="_self">Th33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E5:52"><i><font color="Green">E41</font></i></a>, <a class="txt" href="isocat_1.html#E8:52"><i><font color="Green">E44</font></i></a>, <a class="ref" href="nattra_1.html#T28">NATTRA_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E5:52"><i><font color="Green">E41</font></i></a>, <a class="txt" href="isocat_1.html#E8:52"><i><font color="Green">E44</font></i></a>, <a class="ref" href="nattra_1.html#T28">NATTRA_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="isocat_1.html#K6" target="_self">(#)</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E1:52"><i><font color="Green">E37</font></i></a>, <a class="txt" href="isocat_1.html#E4:52"><i><font color="Green">E40</font></i></a>, <a class="ref" href="isocat_1.html#T41" target="_self">Th41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="isocat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="isocat_1.html#K5" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E8:52"><i><font color="Green">E44</font></i></a>, <a class="txt" href="isocat_1.html#E9:52"><i><font color="Green">E45</font></i></a>, <a class="txt" href="isocat_1.html#E10:52"><i><font color="Green">E46</font></i></a>, <a class="ref" href="nattra_1.html#T28">NATTRA_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="isocat_1.html#K6" target="_self">(#)</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="isocat_1.html#K6" target="_self">(#)</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_1.html#E5:52"><i><font color="Green">E41</font></i></a>, <a class="txt" href="isocat_1.html#E9:52"><i><font color="Green">E45</font></i></a>, <a class="txt" href="isocat_1.html#E11:52"><i><font color="Green">E47</font></i></a>, <a class="txt" href="isocat_1.html#E12:52"><i><font color="Green">E48</font></i></a>, <a class="ref" href="nattra_1.html#T28">NATTRA_1:28</a></i>
;<br/>


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