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<b>let </b><font color="Maroon">It1</font> be  <a href="cat_1.html#V1">strict</a> <a href="nattra_1.html#V2" target="_self">discrete</a>  <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">C</font>, <font color="Maroon">It2</font> be  <a href="cat_1.html#V1">strict</a> <a href="nattra_1.html#V2" target="_self">discrete</a>  <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">C</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:75_1_2"/><i><font color="Green">E50</font></i>: 
( the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">It1</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font> &amp; the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">It1</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : verum </span>}</span>  )
 <b>and </b><br/><a NAME="E2:75_1_2"/><i><font color="Green">E51</font></i>: 
( the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">It2</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font> &amp; the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">It2</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Olive">a</font></span>)</span> where <font color="Olive">a</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font> : verum </span>}</span>  )
 ;<br/>

<b>set </b><font color="Maroon">M</font> = the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">It1</font>;<br/>
<a NAME="E3:75_1_2"/><i><font color="Green">E88</font></i>: 
( the <a href="cat_1.html#U3">Dom</a> of <font color="Maroon">It1</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U3">Dom</a> of <font color="Maroon">C</font> <a href="relat_1.html#K7">|</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">It1</font> &amp; the <a href="cat_1.html#U3">Dom</a> of <font color="Maroon">It2</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U3">Dom</a> of <font color="Maroon">C</font> <a href="relat_1.html#K7">|</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">It1</font> )
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E4:75_1_2"/><i><font color="Green">E93</font></i>: 
( the <a href="cat_1.html#U4">Cod</a> of <font color="Maroon">It1</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U4">Cod</a> of <font color="Maroon">C</font> <a href="relat_1.html#K7">|</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">It1</font> &amp; the <a href="cat_1.html#U4">Cod</a> of <font color="Maroon">It2</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U4">Cod</a> of <font color="Maroon">C</font> <a href="relat_1.html#K7">|</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">It1</font> )
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:75_1_2"/><i><font color="Green">E94</font></i>: 
( the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">It1</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font> <a href="realset1.html#K1">||</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">It1</font> &amp; the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">It2</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U5">Comp</a> of <font color="Maroon">C</font> <a href="realset1.html#K1">||</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">It1</font> )
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E6:75_1_2"/>
( the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">It1</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font> <a href="relat_1.html#K7">|</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">It1</font> &amp; the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">It2</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U6">Id</a> of <font color="Maroon">C</font> <a href="relat_1.html#K7">|</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">It2</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:75_1_2"/>
<font color="Maroon">It1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">It2</font>
 <b>by </b><i>, , , , </i>;<br/>


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