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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="cat_3.html#M1" target="_self">Projections_family</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><a NAME="E1:59"/>
 <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:59"/><b>then </b>
 <a href="cat_3.html#K3" target="_self">doms</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="cat_3.html#K1" target="_self">--&gt;</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="cat_3.html#D14" target="_self">Def14</a></i>;<br/>
<b>hence </b><a NAME="E3:59"/>
 <a href="cat_3.html#K3" target="_self">doms</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_3.html#K7" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="cat_3.html#K1" target="_self">--&gt;</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_3.html#T20" target="_self">Th20</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_3.html#D14" target="_self">CAT_3:def 14</a><br/>


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