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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 <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><a NAME="E1:35"/><i><font color="Green">E32</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>
 ;<br/>

<a NAME="E2:35"/><b>then </b><i><font color="Green">E33</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="ref" href="nattra_1.html#D7">NATTRA_1:def 7</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>6</sub></font>, <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>assume </b><a NAME="E3:35"/><i><font color="Green">E34</font></i>: 
 <a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#R2">=</a>  <a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="cat_1.html#NM1">Object</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>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>10</sub></font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:35_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</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>10</sub></font></span><a href="cat_2.html#K12">]</a></span>
 <b>by </b><i><a class="ref" href="cat_2.html#T35">CAT_2:35</a></i>;<br/><a NAME="E3:35_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>11</sub></font> = <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>12</sub></font> = <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/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="p3">(<span class="default"><span class="p4">(<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><a href="cat_2.html#K12">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<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></span>)</span></span><a href="tarski.html#K4">]</a></span> = 
<span class="p1">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <font color="Maroon">c<sub>6</sub></font></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#E1:35"><i><font color="Green">E32</font></i></a>, <a class="ref" href="isocat_2.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<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="p3">(<span class="default"><span class="p4">(<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><a href="cat_2.html#K12">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<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></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:35"><i><font color="Green">E32</font></i></a>, <a class="txt" href="isocat_2.html#E3:35"><i><font color="Green">E34</font></i></a>, <a class="ref" href="isocat_2.html#D5" target="_self">Def5</a></i>
;<br/><a NAME="E6:35_1"/><b>then </b><i><font color="Green">E36</font></i>: 
<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> <a href="funct_2.html#R2">=</a> <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>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>6</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<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>10</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E2:35"><i><font color="Green">E33</font></i></a>, <a class="txt" href="isocat_2.html#E2:35_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<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></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E6:35_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="cat_2.html#T3">CAT_2:3</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>10</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> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="isocat_2.html#E2:35"><i><font color="Green">E33</font></i></a>, <a class="txt" href="isocat_2.html#E2:35_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:35"/>
<font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="isocat_2.html#E1:35"><i><font color="Green">E32</font></i></a>, <a class="ref" href="isocat_1.html#T31">ISOCAT_1:31</a></i>;<br/>


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