<?xml version="1.0"?>
<div class="add">

<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 <span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="cat_2.html#K11">:]</a></span>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:34"/><i><font color="Green">E31</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="E2:34"/><i><font color="Green">E32</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>
 ;<br/>

<a NAME="E3:34"/><i><font color="Green">E33</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_2.html#E1:34"><i><font color="Green">E31</font></i></a>, <a class="txt" href="isocat_2.html#E2:34"><i><font color="Green">E32</font></i></a>, <a class="ref" href="nattra_1.html#T25">NATTRA_1:25</a></i>;<br/>
<a NAME="E4:34"/><i><font color="Green">E34</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>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E1:34"><i><font color="Green">E31</font></i></a>, <a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/>
<a NAME="E5:34"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E2:34"><i><font color="Green">E32</font></i></a>, <a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/>
<a NAME="E6:34"/><i><font color="Green">E36</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>6</sub></font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E3:34"><i><font color="Green">E33</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>7</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>8</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/>



<a NAME="E7:34"/><i><font color="Green">E37</font></i>: 
 <a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a>  <a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E1:34"><i><font color="Green">E31</font></i></a>, <a class="ref" href="isocat_2.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E8:34"/><b>then </b><i><font color="Green">E38</font></i>: 
 <a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#R1">is_transformable_to</a>  <a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/>
<a NAME="E9:34"/><i><font color="Green">E39</font></i>: 
 <a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a>  <a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E2:34"><i><font color="Green">E32</font></i></a>, <a class="ref" href="isocat_2.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E10:34"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>5</sub></font> <a href="nattra_1.html#R1">is_transformable_to</a>  <a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/>
<a NAME="E11:34"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#R1">is_transformable_to</a>  <a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="isocat_2.html#E8:34"><i><font color="Green">E38</font></i></a>, <a class="ref" href="nattra_1.html#T19">NATTRA_1:19</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><a NAME="E1:34_1"/>
the <a href="cat_1.html#U1">Objects</a> of <span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="cat_2.html#K11">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="cat_2.html#T33">CAT_2:33</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>8</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>7</sub></font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/><b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>9</sub></font> as    <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> <b>by </b><i><a class="ref" href="isocat_2.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E4:34_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="isocat_2.html#T24" target="_self">Th24</a></i>;<br/><a NAME="E5:34_1"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:34"><i><font color="Green">E31</font></i></a>, <a class="ref" href="isocat_2.html#T15" target="_self">Th15</a></i>;<br/><a NAME="E6:34_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E2:34"><i><font color="Green">E32</font></i></a>, <a class="txt" href="isocat_2.html#E4:34_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="isocat_2.html#T15" target="_self">Th15</a></i>;<br/><a NAME="E7:34_1"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="nattra_1.html#R2">is_naturally_transformable_to</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E5:34_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="nattra_1.html#T25">NATTRA_1:25</a></i>;<br/><a NAME="E8:34_1"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/><a NAME="E9:34_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E5:34_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/><a NAME="E10:34_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="nattra_1.html#R1">is_transformable_to</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E6:34_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2">curry</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="cat_2.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> as    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <b>by </b><i><a class="txt" href="isocat_2.html#E1:34"><i><font color="Green">E31</font></i></a>, <a class="txt" href="isocat_2.html#E4:34_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="isocat_2.html#T15" target="_self">Th15</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2">curry</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="cat_2.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> as    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <b>by </b><i><a class="txt" href="isocat_2.html#E2:34"><i><font color="Green">E32</font></i></a>, <a class="txt" href="isocat_2.html#E4:34_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="isocat_2.html#T15" target="_self">Th15</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <span class="p1">(<span class="default"><a href="cat_2.html#K2">curry</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="cat_2.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> as    <a href="nattra_1.html#M2">natural_transformation</a> of <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font> <b>by </b><i><a class="txt" href="isocat_2.html#E3:34"><i><font color="Green">E33</font></i></a>, <a class="txt" href="isocat_2.html#E4:34_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="isocat_2.html#T15" target="_self">Th15</a></i>;<br/><a NAME="E14:34_1"/><i><font color="Green">E48</font></i>: 
<span class="p1">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>17</sub></font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E2:34"><i><font color="Green">E32</font></i></a>, <a class="ref" href="isocat_2.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E15:34_1"/><i><font color="Green">E49</font></i>: 
<span class="p1">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>16</sub></font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:34"><i><font color="Green">E31</font></i></a>, <a class="ref" href="isocat_2.html#D5" target="_self">Def5</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>19</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><a NAME="E1:34_1_1"/><i><font color="Green">E50</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> <span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="cat_2.html#K12">]</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K13">.</a> <span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="cat_2.html#K12">]</a></span></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#E4:34"><i><font color="Green">E34</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/><a NAME="E2:34_1_1"/><i><font color="Green">E51</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> <span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="cat_2.html#K12">]</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K13">.</a> <span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="cat_2.html#K12">]</a></span></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#E5:34"><i><font color="Green">E35</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/><a NAME="E3:34_1_1"/><i><font color="Green">E52</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>19</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#E9:34_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/><a NAME="E4:34_1_1"/><i><font color="Green">E53</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>19</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#E10:34_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/><i><font color="Green">E54</font></i>: <font color="Maroon">c<sub>17</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>19</sub></font> = 
<font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E10:34_1"><i><font color="Green">E47</font></i></a>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="ref" href="cat_2.html#T3">CAT_2:3</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font> <a href="nattra_1.html#K5">.</a> <span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="cat_2.html#K12">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E5:34"><i><font color="Green">E35</font></i></a>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
;<br/><i><font color="Green">E55</font></i>: <font color="Maroon">c<sub>16</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>19</sub></font> = 
<font color="Maroon">c<sub>16</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E9:34_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="ref" href="cat_2.html#T3">CAT_2:3</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K5">.</a> <span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="cat_2.html#K12">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E4:34"><i><font color="Green">E34</font></i></a>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
;<br/><b>thus </b><font color="Maroon">c<sub>18</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>19</sub></font> = 
<font color="Maroon">c<sub>18</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E8:34_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
<br/>.= 
<font color="Maroon">c<sub>12</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="ref" href="cat_2.html#T3">CAT_2:3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="cat_2.html#K12">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E6:34"><i><font color="Green">E36</font></i></a>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nattra_1.html#K5">.</a> <span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="cat_2.html#K12">]</a></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#K5">.</a> <span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>19</sub></font></span><a href="cat_2.html#K12">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:34"><i><font color="Green">E31</font></i></a>, <a class="txt" href="isocat_2.html#E2:34"><i><font color="Green">E32</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>17</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:34_1_1"><i><font color="Green">E50</font></i></a>, <a class="txt" href="isocat_2.html#E2:34_1_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="isocat_2.html#E5:34_1_1"><i><font color="Green">E54</font></i></a>, <a class="txt" href="isocat_2.html#E6:34_1_1"><i><font color="Green">E55</font></i></a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:34_1_1"><i><font color="Green">E52</font></i></a>, <a class="txt" href="isocat_2.html#E4:34_1_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E5:34_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="isocat_2.html#E6:34_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="nattra_1.html#T27">NATTRA_1:27</a></i>
;<br/></div><b>end;</b></div><a NAME="E17:34_1"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E8:34_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="nattra_1.html#T20">NATTRA_1:20</a></i>;<br/><a NAME="E18:34_1"/><i><font color="Green">E51</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>9</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#E8:34"><i><font color="Green">E38</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/><a NAME="E19:34_1"/><i><font color="Green">E52</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>9</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#E10:34"><i><font color="Green">E40</font></i></a>, <a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>18</sub></font></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E3:34"><i><font color="Green">E33</font></i></a>, <a class="ref" href="isocat_2.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E14:34_1"><i><font color="Green">E48</font></i></a>, <a class="txt" href="isocat_2.html#E15:34_1"><i><font color="Green">E49</font></i></a>, <a class="txt" href="isocat_2.html#E17:34_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="nattra_1.html#T42">NATTRA_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E18:34_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="isocat_2.html#E19:34_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p2">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E7:34"><i><font color="Green">E37</font></i></a>, <a class="txt" href="isocat_2.html#E9:34"><i><font color="Green">E39</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="E13:34"/>
 <a href="isocat_2.html#K6" target="_self">export</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nattra_1.html#K8">`*`</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="nattra_1.html#K8">`*`</a> <span class="p1">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="isocat_2.html#E11:34"><i><font color="Green">E41</font></i></a>, <a class="ref" href="nattra_1.html#T20">NATTRA_1:20</a></i>;<br/>


</div>
