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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> 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>6</sub></font>, <font color="Maroon">c<sub>7</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>3</sub></font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:56"/><i><font color="Green">E51</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="E2:56"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E3:56"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="isocat_2.html#E1:56"><i><font color="Green">E51</font></i></a>, <a class="txt" href="isocat_2.html#E2:56"><i><font color="Green">E52</font></i></a>, <a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<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>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E4:56"/><i><font color="Green">E54</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>;<br/>

<a NAME="E5:56"/><i><font color="Green">E55</font></i>: 
( <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>11</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_1.html#K9">*</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> &amp; <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>11</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</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="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_1.html#K9">*</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> )
 
<b>by </b><i><a class="txt" href="isocat_2.html#E1:56"><i><font color="Green">E51</font></i></a>, <a class="txt" href="isocat_2.html#E2:56"><i><font color="Green">E52</font></i></a>, <a class="txt" href="isocat_2.html#E4:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="nattra_1.html#D8">NATTRA_1:def 8</a></i>;<br/>
<a NAME="E6:56"/><i><font color="Green">E56</font></i>: 
<span class="p1"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><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>11</sub></font></span>)</span>,<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>11</sub></font></span>)</span></span><a href="cat_2.html#K13">]</a></span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:56"><i><font color="Green">E53</font></i></a>, <a class="ref" href="isocat_2.html#T45" target="_self">Th45</a></i>;<br/>
<a NAME="E7:56"/><i><font color="Green">E57</font></i>: 
<span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span><a href="cat_2.html#K13">]</a></span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E4:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="isocat_2.html#T42" target="_self">Th42</a></i>;<br/>
<a NAME="E8:56"/><i><font color="Green">E58</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>11</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>11</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_2.html#E3:56"><i><font color="Green">E53</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/>
<a NAME="E9:56"/><i><font color="Green">E59</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>4</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</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_2.html#E4:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="cat_1.html#T126">CAT_1:126</a></i>;<br/>
<a NAME="E10:56"/><i><font color="Green">E60</font></i>: 
 <a href="cat_1.html#K6">Hom</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>,<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>11</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_2.html#E4:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="cat_1.html#T126">CAT_1:126</a></i>;<br/>
<a NAME="E11:56"/><i><font color="Green">E61</font></i>: 
 <a href="cat_1.html#K6">Hom</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>11</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</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_2.html#E3:56"><i><font color="Green">E53</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/>
<a NAME="E12:56"/><i><font color="Green">E62</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> 
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:56"><i><font color="Green">E53</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/>
<a NAME="E13:56"/><i><font color="Green">E63</font></i>: 
 <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>5</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</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_2.html#E4:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="cat_1.html#T126">CAT_1:126</a></i>;<br/>
<a NAME="E14:56"/><i><font color="Green">E64</font></i>: 
 <a href="cat_1.html#K6">Hom</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>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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_2.html#E3:56"><i><font color="Green">E53</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/>
<a NAME="E15:56"/><i><font color="Green">E65</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</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>7</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</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_2.html#E4:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="cat_1.html#T126">CAT_1:126</a></i>;<br/>
<i><font color="Green">E66</font></i>:  <a href="cat_1.html#K2">dom</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>11</sub></font></span>)</span> = 
<font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E8:56"><i><font color="Green">E58</font></i></a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
<br/>.= 
 <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E9:56"><i><font color="Green">E59</font></i></a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
;<br/>
<i><font color="Green">E67</font></i>:  <a href="cat_1.html#K2">dom</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>11</sub></font></span>)</span> = 
<font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E11:56"><i><font color="Green">E61</font></i></a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
<br/>.= 
 <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E10:56"><i><font color="Green">E60</font></i></a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
;<br/>
<a NAME="E18:56"/><i><font color="Green">E68</font></i>: 
<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>11</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="hidden.html#R1">=</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>11</sub></font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E8:56"><i><font color="Green">E58</font></i></a>, <a class="txt" href="isocat_2.html#E9:56"><i><font color="Green">E59</font></i></a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>;<br/>
<a NAME="E19:56"/><i><font color="Green">E69</font></i>: 
<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>11</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="hidden.html#R1">=</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>11</sub></font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E10:56"><i><font color="Green">E60</font></i></a>, <a class="txt" href="isocat_2.html#E11:56"><i><font color="Green">E61</font></i></a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>;<br/>
<a NAME="E20:56"/><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_1.html#K9">*</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>5</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_1.html#K4">*</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>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E12:56"><i><font color="Green">E62</font></i></a>, <a class="txt" href="isocat_2.html#E13:56"><i><font color="Green">E63</font></i></a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>;<br/>
<a NAME="E21:56"/><i><font color="Green">E71</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_1.html#K9">*</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="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_1.html#K4">*</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>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E14:56"><i><font color="Green">E64</font></i></a>, <a class="txt" href="isocat_2.html#E15:56"><i><font color="Green">E65</font></i></a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>;<br/>
<i><font color="Green">E72</font></i>:  <a href="cat_1.html#K3">cod</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> = 
<font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E12:56"><i><font color="Green">E62</font></i></a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
<br/>.= 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E13:56"><i><font color="Green">E63</font></i></a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
;<br/>
<i><font color="Green">E73</font></i>:  <a href="cat_1.html#K3">cod</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> = 
<font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E14:56"><i><font color="Green">E64</font></i></a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
<br/>.= 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E15:56"><i><font color="Green">E65</font></i></a>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a></i>
;<br/>
<a NAME="E24:56"/><i><font color="Green">E74</font></i>: 
<span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span><a href="cat_2.html#K13">]</a></span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E4:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="isocat_2.html#T42" target="_self">Th42</a></i>;<br/>
<a NAME="E25:56"/><i><font color="Green">E75</font></i>: 
<span class="p1"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><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 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><a href="cat_2.html#K13">]</a></span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:56"><i><font color="Green">E53</font></i></a>, <a class="ref" href="isocat_2.html#T45" target="_self">Th45</a></i>;<br/>
<a NAME="E26:56"/><i><font color="Green">E76</font></i>: 
<span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#R1">is_transformable_to</a> <span class="p1"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:56"><i><font color="Green">E53</font></i></a>, <a class="ref" href="isocat_2.html#T44" target="_self">Th44</a></i>;<br/>
<a NAME="E27:56"/><b>then </b><i><font color="Green">E77</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <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="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/>
<a NAME="E28:56"/><i><font color="Green">E78</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</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_2.html#E4:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="cat_1.html#T126">CAT_1:126</a></i>;<br/>
<a NAME="E29:56"/><i><font color="Green">E79</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</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_2.html#E4:56"><i><font color="Green">E54</font></i></a>, <a class="ref" href="cat_1.html#T126">CAT_1:126</a></i>;<br/>
<a NAME="E30:56"/>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>11</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_2.html#E26:56"><i><font color="Green">E76</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E29:56"><i><font color="Green">E79</font></i></a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p3">(<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>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p3">(<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></span><a href="cat_2.html#K13">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E5:56"><i><font color="Green">E55</font></i></a>, <a class="txt" href="isocat_2.html#E6:56"><i><font color="Green">E56</font></i></a>, <a class="txt" href="isocat_2.html#E7:56"><i><font color="Green">E57</font></i></a>, <a class="txt" href="isocat_2.html#E16:56"><i><font color="Green">E66</font></i></a>, <a class="txt" href="isocat_2.html#E17:56"><i><font color="Green">E67</font></i></a>, <a class="txt" href="isocat_2.html#E18:56"><i><font color="Green">E68</font></i></a>, <a class="txt" href="isocat_2.html#E19:56"><i><font color="Green">E69</font></i></a>, <a class="ref" href="cat_2.html#T39">CAT_2:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></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_2.html#E20:56"><i><font color="Green">E70</font></i></a>, <a class="txt" href="isocat_2.html#E21:56"><i><font color="Green">E71</font></i></a>, <a class="txt" href="isocat_2.html#E22:56"><i><font color="Green">E72</font></i></a>, <a class="txt" href="isocat_2.html#E23:56"><i><font color="Green">E73</font></i></a>, <a class="txt" href="isocat_2.html#E24:56"><i><font color="Green">E74</font></i></a>, <a class="txt" href="isocat_2.html#E25:56"><i><font color="Green">E75</font></i></a>, <a class="ref" href="cat_2.html#T39">CAT_2:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K10" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="isocat_2.html#K10" target="_self">:&gt;</a></span> <a href="nattra_1.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="isocat_2.html#K15" target="_self">&lt;:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="isocat_2.html#K15" target="_self">:&gt;</a></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_2.html#E27:56"><i><font color="Green">E77</font></i></a>, <a class="txt" href="isocat_2.html#E28:56"><i><font color="Green">E78</font></i></a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
;<br/><br/>


</div>
