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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b1">f</font></span>)</span></span><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">,?&gt;</a></span>,<span class="p3"><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">f</font></span>)</span></span><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">,?&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="yoneda_1.html#K3" title="YONEDA_1:func.3">&lt;|</a><span class="default"><font color="Olive" title="b1">f</font></span><a href="yoneda_1.html#K3" title="YONEDA_1:func.3">,?&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c1">A</font>,<span class="p2">(<span class="default"><a href="yoneda_1.html#K1" title="YONEDA_1:func.1">EnsHom</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">,?&gt;</a></span>,<span class="p3"><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">,?&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="yoneda_1.html#K3" title="YONEDA_1:func.3">&lt;|</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="yoneda_1.html#K3" title="YONEDA_1:func.3">,?&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c1">A</font>,<span class="p2">(<span class="default"><a href="yoneda_1.html#K1" title="YONEDA_1:func.1">EnsHom</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span></span><br/>



<a NAME="E1:6"/>
<span class="p1"><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">&lt;|</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">,?&gt;</a></span> <a href="nattra_1.html#R2" title="NATTRA_1:pred.2">is_naturally_transformable_to</a> <span class="p1"><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">&lt;|</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">,?&gt;</a></span>
 
<b>by </b><i><a class="ref" href="yoneda_1.html#T3" target="_self" title="YONEDA_1:th.3">Th3</a></i>;<br/>
<a NAME="E2:6"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">,?&gt;</a></span>,<span class="p3"><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">,?&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="yoneda_1.html#K3" title="YONEDA_1:func.3">&lt;|</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="yoneda_1.html#K3" title="YONEDA_1:func.3">,?&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="nattra_1.html#K11" title="NATTRA_1:func.11">NatTrans</a> <font color="Maroon" title="c1">A</font>,<span class="p1">(<span class="default"><a href="yoneda_1.html#K1" title="YONEDA_1:func.1">EnsHom</a> <font color="Maroon" title="c1">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D16" title="NATTRA_1:def.16">NATTRA_1:def 16</a></i>;<br/>
<b>hence </b><a NAME="E3:6"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">,?&gt;</a></span>,<span class="p3"><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">&lt;|</a><span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="yoneda_1.html#K2" title="YONEDA_1:func.2">,?&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="yoneda_1.html#K3" title="YONEDA_1:func.3">&lt;|</a><span class="default"><font color="Maroon" title="c2">f</font></span><a href="yoneda_1.html#K3" title="YONEDA_1:func.3">,?&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" title="NATTRA_1:func.12">Functors</a> <font color="Maroon" title="c1">A</font>,<span class="p2">(<span class="default"><a href="yoneda_1.html#K1" title="YONEDA_1:func.1">EnsHom</a> <font color="Maroon" title="c1">A</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nattra_1.html#D18" title="NATTRA_1:def.18">NATTRA_1:def 18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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