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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="cat_5.html#V3">Categorial</a> <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:4"/><i><font color="Green">E1</font></i>: 
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:4"/><i><font color="Green">E2</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="cat_5.html#K8">`11</a>  <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="cat_5.html#K9">`12</a>  <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="cat_5.html#K8">`11</a>  <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="cat_5.html#K9">`12</a>  <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="cat_5.html#T13">CAT_5:13</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>3</sub></font> <a href="cat_5.html#K8">`11</a> ,<font color="Maroon">c<sub>3</sub></font> <a href="cat_5.html#K9">`12</a> <b> such that </b><br/><a NAME="E4:4"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="cat_2.html#K12">]</a></span>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="cat_5.html#D6">CAT_5:def 6</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>2</sub></font> <a href="cat_5.html#K8">`11</a> ,<font color="Maroon">c<sub>3</sub></font> <a href="cat_5.html#K8">`11</a> <b> such that </b><br/><a NAME="E6:4"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="cat_2.html#K12">]</a></span>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="txt" href="index_1.html#E1:4"><i><font color="Green">E1</font></i></a>, <a class="txt" href="index_1.html#E2:4"><i><font color="Green">E2</font></i></a>, <a class="ref" href="cat_5.html#D6">CAT_5:def 6</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="cat_2.html#K12">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="index_1.html#E1:4"><i><font color="Green">E1</font></i></a>, <a class="txt" href="index_1.html#E2:4"><i><font color="Green">E2</font></i></a>, <a class="txt" href="index_1.html#E4:4"><i><font color="Green">E3</font></i></a>, <a class="txt" href="index_1.html#E6:4"><i><font color="Green">E4</font></i></a>, <a class="ref" href="cat_5.html#D6">CAT_5:def 6</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="cat_2.html#K12">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="index_1.html#K1" target="_self">`2</a> </span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="index_1.html#E6:4"><i><font color="Green">E4</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="cat_2.html#K12">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="index_1.html#K1" target="_self">`2</a> </span>)</span> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="index_1.html#K1" target="_self">`2</a> </span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="index_1.html#E4:4"><i><font color="Green">E3</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
;<br/>


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