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<b>let </b><font color="Maroon">o</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>thus </b><a NAME="E1:12_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U1">Objects</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K8">1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span> implies <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font> )
 <b>by </b><i><a class="ref" href="cat_1.html#T34">CAT_1:34</a></i>;<br/><a NAME="E2:12_1"/>
<font color="Maroon">o</font> is   <a href="cat_1.html#NM1">Object</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K8">1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#T32">CAT_1:32</a></i>;<br/><b>hence </b><a NAME="E3:12_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font> implies <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U1">Objects</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K8">1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:12"/>
the <a href="cat_1.html#U1">Objects</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K8">1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">o</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>thus </b><a NAME="E1:12_2"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K8">1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span> implies <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> )
 <b>by </b><i><a class="ref" href="cat_1.html#T35">CAT_1:35</a></i>;<br/><a NAME="E2:12_2"/>
<font color="Maroon">m</font> is   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K8">1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#T33">CAT_1:33</a></i>;<br/><b>hence </b><a NAME="E3:12_2"/>
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> implies <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K8">1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:12"/>
the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1">(<span class="default"><a href="cat_1.html#K8">1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">m</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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