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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</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="graph_1.html#K4" title="GRAPH_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="graph_1.html#K3" title="GRAPH_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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K9" title="NATTRA_1:func.9">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/><span class="kw">let </span><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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="graph_1.html#K4" title="GRAPH_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="graph_1.html#K3" title="GRAPH_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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K9" title="NATTRA_1:func.9">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="graph_1.html#K4" title="GRAPH_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="graph_1.html#K3" title="GRAPH_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 class="kw">by</span> <span class="lab"><a class="ref" href="yoneda_1.html#T2" target="_self" onmouseover="rs('yoneda_1/T2')" onmouseout="rh()">Th2</a></span>;<br/>
<a NAME="E2:6"/><span class="kw">then </span>
<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="graph_1.html#K4" title="GRAPH_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="graph_1.html#K3" title="GRAPH_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#K8" title="NATTRA_1:func.8">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>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D16" onmouseover="rs('nattra_1/D16')" onmouseout="rh()">NATTRA_1:def 16</a></span>;<br/>
<span class="kw">hence </span><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="graph_1.html#K4" title="GRAPH_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="graph_1.html#K3" title="GRAPH_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="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K9" title="NATTRA_1:func.9">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 class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D17" onmouseover="rs('nattra_1/D17')" onmouseout="rh()">NATTRA_1:def 17</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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