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

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="nattra_1.html#M2">natural_transformation</a> of <span class="p1"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span>,<span class="p1"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:5_1_2"/><i><font color="Green">E4</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>3</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Olive">b<sub>1</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"><span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22">hom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E2:5_1_2"/><i><font color="Green">E5</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Olive">b<sub>1</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"><span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22">hom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<a NAME="E3:5_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font> holds <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K19">hom</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<i><font color="Green">E6</font></i>:  <a href="yoneda_1.html#K1" target="_self">EnsHom</a> <font color="Maroon">c<sub>1</sub></font> = 
 <a href="ens_1.html#K12">Ens</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<br/>.= 
 <a href="cat_1.html#G1">CatStr</a>(# <span class="p1">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="ens_1.html#K2">Maps</a> <span class="p2">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ens_1.html#K8">fDom</a> <span class="p2">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ens_1.html#K9">fCod</a> <span class="p2">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ens_1.html#K10">fComp</a> <span class="p2">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ens_1.html#K11">fId</a> <span class="p2">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> #)
<b>by </b><i><a class="ref" href="ens_1.html#D14">ENS_1:def 14</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>6</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"><span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K19">hom</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> as   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="yoneda_1.html#K1" target="_self">EnsHom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="ens_1.html#T48">ENS_1:48</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="subset_1.html#M1">Element</a> of  <a href="ens_1.html#K2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="ens_1.html#T48">ENS_1:48</a></i>;<br/>
<i><font color="Green">E7</font></i>:  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><a href="ens_1.html#K8">fDom</a> <span class="p2">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="yoneda_1.html#E1:5_1_2_1"><i><font color="Green">E6</font></i></a>, <a class="ref" href="cat_1.html#D2">CAT_1:def 2</a></i>
<br/>.= 
 <a href="ens_1.html#K3">dom</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="ens_1.html#D10">ENS_1:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="ref" href="ens_1.html#D4">ENS_1:def 4</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <span class="p2">(<span class="default"><a href="ens_1.html#K24">hom?-</a> <span class="p3">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="ens_1.html#T60">ENS_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ens_1.html#K24">hom?-</a> <span class="p2">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="cat_1.html#D20">CAT_1:def 20</a></i>
<br/>.= 
<span class="p1"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="ens_1.html#D26">ENS_1:def 26</a></i>
;<br/>
 <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><a href="ens_1.html#K9">fCod</a> <span class="p2">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="yoneda_1.html#E1:5_1_2_1"><i><font color="Green">E6</font></i></a>, <a class="ref" href="cat_1.html#D3">CAT_1:def 3</a></i>
<br/>.= 
 <a href="ens_1.html#K4">cod</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="ens_1.html#D11">ENS_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i><a class="ref" href="ens_1.html#D5">ENS_1:def 5</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a> 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <span class="p2">(<span class="default"><a href="ens_1.html#K24">hom?-</a> <span class="p3">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="ens_1.html#T60">ENS_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ens_1.html#K24">hom?-</a> <span class="p2">(<span class="default"><a href="ens_1.html#K17">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="cat_1.html#D20">CAT_1:def 20</a></i>
<br/>.= 
<span class="p1"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="ens_1.html#D26">ENS_1:def 26</a></i>
;<br/>
<b>hence </b><a NAME="E6:5_1_2_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K19">hom</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="yoneda_1.html#E4:5_1_2_1"><i><font color="Green">E7</font></i></a>, <a class="ref" href="cat_1.html#T18">CAT_1:18</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:5_1_2"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font> holds  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span> <a href="cat_1.html#K13">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
;<br/>
<a NAME="E5:5_1_2"/><b>then </b><i><font color="Green">E6</font></i>: 
<span class="p1"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span> <a href="nattra_1.html#R1">is_transformable_to</a> <span class="p1"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D2">NATTRA_1:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>5</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"><span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22">hom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="yoneda_1.html#E1:5_1_2"><i><font color="Green">E4</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="yoneda_1.html#E2:5_1_2"><i><font color="Green">E5</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:5_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="yoneda_1.html#E5:5_1_2"><i><font color="Green">E6</font></i></a>, <a class="ref" href="nattra_1.html#T20">NATTRA_1:20</a></i>;<br/>


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