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<b>let </b><font color="Maroon" title="c2">It1</font>, <font color="Maroon" title="c3">It2</font> be  <a href="cat_1.html#V1" title="CAT_1:attr.1">strict</a> <a href="nattra_1.html#V2" title="NATTRA_1:attr.2">discrete</a>  <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c1">C</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:74_1_2"/><i><font color="Green" title="E56">A22</font></i>: 
( the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c2">It1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> &amp; the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">It1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> : verum </span>}</span>  )
 <b>and </b><br/><a NAME="E2:74_1_2"/><i><font color="Green" title="E57">A23</font></i>: 
( the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c3">It2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> &amp; the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c3">It2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> : verum </span>}</span>  )
 ;<br/>

<b>set </b><font color="Maroon" title="c4">M</font> = the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">It1</font>;<br/>
<a NAME="E3:74_1_2"/><i><font color="Green" title="E58">A24</font></i>: 
( the <a href="cat_1.html#U3" title="CAT_1:sel.3">Dom</a> of <font color="Maroon" title="c2">It1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U3" title="CAT_1:sel.3">Dom</a> of <font color="Maroon" title="c1">C</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">It1</font> &amp; the <a href="cat_1.html#U3" title="CAT_1:sel.3">Dom</a> of <font color="Maroon" title="c3">It2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U3" title="CAT_1:sel.3">Dom</a> of <font color="Maroon" title="c1">C</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">It1</font> )
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:74_1_2"><i><font color="Green" title="E56">A22</font></i></a>, <a class="txt" href="nattra_1.html#E2:74_1_2"><i><font color="Green" title="E57">A23</font></i></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>;<br/>
<a NAME="E4:74_1_2"/><i><font color="Green" title="E59">A25</font></i>: 
( the <a href="cat_1.html#U4" title="CAT_1:sel.4">Cod</a> of <font color="Maroon" title="c2">It1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U4" title="CAT_1:sel.4">Cod</a> of <font color="Maroon" title="c1">C</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">It1</font> &amp; the <a href="cat_1.html#U4" title="CAT_1:sel.4">Cod</a> of <font color="Maroon" title="c3">It2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U4" title="CAT_1:sel.4">Cod</a> of <font color="Maroon" title="c1">C</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">It1</font> )
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:74_1_2"><i><font color="Green" title="E56">A22</font></i></a>, <a class="txt" href="nattra_1.html#E2:74_1_2"><i><font color="Green" title="E57">A23</font></i></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>;<br/>
<a NAME="E5:74_1_2"/><i><font color="Green" title="E60">A26</font></i>: 
( the <a href="cat_1.html#U5" title="CAT_1:sel.5">Comp</a> of <font color="Maroon" title="c2">It1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U5" title="CAT_1:sel.5">Comp</a> of <font color="Maroon" title="c1">C</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">It1</font> &amp; the <a href="cat_1.html#U5" title="CAT_1:sel.5">Comp</a> of <font color="Maroon" title="c3">It2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U5" title="CAT_1:sel.5">Comp</a> of <font color="Maroon" title="c1">C</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">It1</font> )
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:74_1_2"><i><font color="Green" title="E56">A22</font></i></a>, <a class="txt" href="nattra_1.html#E2:74_1_2"><i><font color="Green" title="E57">A23</font></i></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>;<br/>
<a NAME="E6:74_1_2"/>
( the <a href="cat_1.html#U6" title="CAT_1:sel.6">Id</a> of <font color="Maroon" title="c2">It1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U6" title="CAT_1:sel.6">Id</a> of <font color="Maroon" title="c1">C</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c2">It1</font> &amp; the <a href="cat_1.html#U6" title="CAT_1:sel.6">Id</a> of <font color="Maroon" title="c3">It2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U6" title="CAT_1:sel.6">Id</a> of <font color="Maroon" title="c1">C</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Objects</a> of <font color="Maroon" title="c3">It2</font> )
 
<b>by </b><i><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>;<br/>
<b>hence </b><a NAME="E7:74_1_2"/>
<font color="Maroon" title="c2">It1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">It2</font>
 <b>by </b><i><a class="txt" href="nattra_1.html#E1:74_1_2"><i><font color="Green" title="E56">A22</font></i></a>, <a class="txt" href="nattra_1.html#E2:74_1_2"><i><font color="Green" title="E57">A23</font></i></a>, <a class="txt" href="nattra_1.html#E3:74_1_2"><i><font color="Green" title="E58">A24</font></i></a>, <a class="txt" href="nattra_1.html#E4:74_1_2"><i><font color="Green" title="E59">A25</font></i></a>, <a class="txt" href="nattra_1.html#E5:74_1_2"><i><font color="Green" title="E60">A26</font></i></a></i>;<br/>


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