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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="oppcat_1.html#M1">Contravariant_Functor</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="nattra_1.html#K12">Functors</a> <font color="Maroon">c<sub>1</sub></font>,<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>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:7_1_2"/><i><font color="Green">E6</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</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"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span>,<span class="p3"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="yoneda_1.html#K3" target="_self">&lt;|</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="yoneda_1.html#K3" target="_self">,?&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E2:7_1_2"/><i><font color="Green">E7</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</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"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span>,<span class="p3"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="yoneda_1.html#K3" target="_self">&lt;|</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="yoneda_1.html#K3" target="_self">,?&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</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"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span>,<span class="p3"><a href="yoneda_1.html#K2" target="_self">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="yoneda_1.html#K2" target="_self">,?&gt;</a></span></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="yoneda_1.html#K3" target="_self">&lt;|</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="yoneda_1.html#K3" target="_self">,?&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="yoneda_1.html#E1:7_1_2"><i><font color="Green">E6</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="yoneda_1.html#E2:7_1_2"><i><font color="Green">E7</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:7_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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