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<b>let </b><font color="Maroon" title="c1">C</font> be  <a href="cat_5.html#V3" title="CAT_5:attr.3">Categorial</a> <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>;<br/>



<b>assume </b><a NAME="E1:4"/><i><font color="Green" title="E1">A1</font></i>: 
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c2">f</font>
 ;<br/>

<a NAME="E2:4"/><i><font color="Green" title="E2">A2</font></i>: 
( <font color="Maroon" title="c3">g</font> <a href="cat_5.html#K8" title="CAT_5:func.8">`11</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">g</font> &amp; <font color="Maroon" title="c3">g</font> <a href="cat_5.html#K9" title="CAT_5:func.9">`12</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c3">g</font> &amp; <font color="Maroon" title="c2">f</font> <a href="cat_5.html#K8" title="CAT_5:func.8">`11</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c2">f</font> &amp; <font color="Maroon" title="c2">f</font> <a href="cat_5.html#K9" title="CAT_5:func.9">`12</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c2">f</font> )
 
<b>by </b><i><a class="ref" href="cat_5.html#T13" title="CAT_5:th.13">CAT_5:13</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">gg</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">g</font> <a href="cat_5.html#K8" title="CAT_5:func.8">`11</a> ,<font color="Maroon" title="c3">g</font> <a href="cat_5.html#K9" title="CAT_5:func.9">`12</a> <b> such that </b><br/><a NAME="E4:4"/><i><font color="Green" title="E3">A3</font></i>: 
<font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">g</font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<font color="Maroon" title="c4">gg</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="cat_5.html#D6" title="CAT_5:def.6">CAT_5:def 6</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">ff</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">f</font> <a href="cat_5.html#K8" title="CAT_5:func.8">`11</a> ,<font color="Maroon" title="c3">g</font> <a href="cat_5.html#K8" title="CAT_5:func.8">`11</a> <b> such that </b><br/><a NAME="E6:4"/><i><font color="Green" title="E4">A4</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<font color="Maroon" title="c5">ff</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="index_1.html#E1:4"><i><font color="Green" title="E1">A1</font></i></a>, <a class="txt" href="index_1.html#E2:4"><i><font color="Green" title="E2">A2</font></i></a>, <a class="ref" href="cat_5.html#D6" title="CAT_5:def.6">CAT_5:def 6</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c3">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c2">f</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">gg</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c5">ff</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="index_1.html#E1:4"><i><font color="Green" title="E1">A1</font></i></a>, <a class="txt" href="index_1.html#E2:4"><i><font color="Green" title="E2">A2</font></i></a>, <a class="txt" href="index_1.html#E4:4"><i><font color="Green" title="E3">A3</font></i></a>, <a class="txt" href="index_1.html#E6:4"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="cat_5.html#D6" title="CAT_5:def.6">CAT_5:def 6</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">gg</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="index_1.html#K1" title="INDEX_1:func.1">`2</a> </span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="index_1.html#E6:4"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="index_1.html#K1" title="INDEX_1:func.1">`2</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="index_1.html#K1" title="INDEX_1:func.1">`2</a> </span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="index_1.html#E4:4"><i><font color="Green" title="E3">A3</font></i></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
;<br/>


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