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<b>let </b><font color="Maroon">A</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/>





<b>assume </b><a NAME="E1:9"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">F</font> is <a href="funct_1.html#V2">one-to-one</a>
 ;<br/>

<b>let </b><font color="Maroon">x1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a><br/>

<b>assume </b><a NAME="E2:9"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">F</font></span>)</span> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">F</font></span>)</span> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">a1</font> = <font color="Maroon">x1</font>, <font color="Maroon">a2</font> = <font color="Maroon">x2</font> as   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font> ;<br/>
<a NAME="E4:9"/><i><font color="Green">E19</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>assume </b><a NAME="E5:9"/>
<span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font>
 ;<br/>

<a NAME="E6:9"/><b>then </b>
<font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a2</font>
 
;<br/>
<b>then </b><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font></span>)</span> = 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a2</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T108">CAT_1:108</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T108">CAT_1:108</a></i>
;<br/>
<a NAME="E8:9"/><b>then </b>
 <a href="cat_1.html#K10">id</a> <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">a2</font>
 
<b>by </b><i>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E9:9"/>
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font>
 <b>by </b><i><a class="ref" href="cat_1.html#T45">CAT_1:45</a></i>;<br/>


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