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<b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="index_1.html#NM10">coIndexing</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">c1</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>, <font color="Maroon">c2</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/>





<b>assume </b><a NAME="E1:43"/><i><font color="Green">E23</font></i>: 
not  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c1</font>,<font color="Maroon">c2</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>let </b><font color="Maroon">m</font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c1</font>,<font color="Maroon">c2</font>;<br/>

<a NAME="E2:43"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="cat_1.html#U3">Dom</a> of <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="cat_1.html#U4">Cod</a> of <font color="Maroon">C</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c2</font> )
 
<b>by </b><i>, <a class="ref" href="cat_1.html#T23">CAT_1:23</a>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E3:43"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="cat_1.html#U3">Dom</a> of <font color="Maroon">C</font></span>)</span> <a href="index_1.html#K2" target="_self">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="index_1.html#K2" target="_self">.</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U3">Dom</a> of <font color="Maroon">C</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font></span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="cat_1.html#U4">Cod</a> of <font color="Maroon">C</font></span>)</span> <a href="index_1.html#K2" target="_self">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="index_1.html#K2" target="_self">.</a> <span class="p1">(<span class="default">the <a href="cat_1.html#U4">Cod</a> of <font color="Maroon">C</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font></span>)</span> &amp; the <a href="cat_1.html#U3">Dom</a> of <font color="Maroon">C</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c1</font> &amp; the <a href="cat_1.html#U4">Cod</a> of <font color="Maroon">C</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c2</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>
<b>hence </b><a NAME="E4:43"/>
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K14" target="_self">`2</a> </span>)</span> <a href="index_1.html#K13" target="_self">.</a> <font color="Maroon">m</font> is    <a href="cat_1.html#M2">Functor</a> of <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="index_1.html#K2" target="_self">.</a> <font color="Maroon">c2</font>,<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K10" target="_self">`1</a> </span>)</span> <a href="index_1.html#K2" target="_self">.</a> <font color="Maroon">c1</font>
 ;<br/>


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