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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a> <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c2">C</font> be    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">C</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">NATTRA_1:def 19</a><br/>





<b>reconsider </b><font color="Maroon" title="c4">f'</font> = <font color="Maroon" title="c3">f</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="cat_2.html#T14" title="CAT_2:th.14">CAT_2:14</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">a'</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E3:68"/><i><font color="Green" title="E54">A1</font></i>: 
<font color="Maroon" title="c4">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c5">a'</font>
 <b>by </b><i><a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def19</a></i>;<br/>
<b>take </b>
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">f</font>
;<br/>

<a NAME="E4:68"/>
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c4">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a'</font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E3:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="cat_1.html#T44" title="CAT_1:th.44">CAT_1:44</a></i>;<br/>
<a NAME="E5:68"/><b>then </b>
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a'</font>
 
<b>by </b><i><a class="ref" href="cat_2.html#T15" title="CAT_2:th.15">CAT_2:15</a></i>;<br/>
<b>hence </b><a NAME="E6:68"/>
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="nattra_1.html#E3:68"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="cat_2.html#D4" title="CAT_2:def.4">CAT_2:def 4</a></i>;<br/>


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