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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c2">i</font>, <font color="Maroon" title="c3">j</font>, <font color="Maroon" title="c4">k</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>;<br/><b>let </b><font color="Maroon" title="c5">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c4">k</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font></span>)</span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
 ;<br/>

<a NAME="E2:20"/><b>then </b><i><font color="Green" title="E7">A2</font></i>: 
( <font color="Maroon" title="c5">e</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c4">k</font> &amp; <font color="Maroon" title="c5">e</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c3">j</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T10" title="MCART_1:th.10">MCART_1:10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">y</font> = <font color="Maroon" title="c5">e</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> , <font color="Maroon" title="c7">x</font> = <font color="Maroon" title="c5">e</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="txt" href="altcat_2.html#E1:20"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="mcart_1.html#T10" title="MCART_1:th.10">MCART_1:10</a></i>;<br/>
<a NAME="E4:20"/><i><font color="Green" title="E8">A3</font></i>: 
<font color="Maroon" title="c5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">x</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<b>by </b><i><a class="txt" href="altcat_2.html#E1:20"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="mcart_1.html#T23" title="MCART_1:th.23">MCART_1:23</a></i>;<br/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c6">y</font> = 
<font color="Maroon" title="c3">j</font>
<b>by </b><i><a class="txt" href="altcat_2.html#E2:20"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="cat_1.html#T18" title="CAT_1:th.18">CAT_1:18</a></i>
<br/>.= 
 <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="altcat_2.html#E2:20"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="cat_1.html#T18" title="CAT_1:th.18">CAT_1:18</a></i>
;<br/>
<b>hence </b><a NAME="E6:20"/>
<font color="Maroon" title="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font>
 <b>by </b><i><a class="txt" href="altcat_2.html#E4:20"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="cat_1.html#T40" title="CAT_1:th.40">CAT_1:40</a></i>;<br/>


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