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<b>let </b><font color="Maroon">A</font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">C</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">A</font>;<br/>



<a NAME="E1:34"/><i><font color="Green">E25</font></i>: 
the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K10">incl</a> <font color="Maroon">C</font></span>)</span> <a href="pboole.html#R6">=</a>  <a href="msualg_3.html#K2">id</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="functor0.html#D29">FUNCTOR0:def 29</a></i>;<br/>
<b>let </b><font color="Maroon">a</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font>, <font color="Maroon">b</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font>;<br/>

<b>assume </b><a NAME="E2:34"/><i><font color="Green">E32</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>let </b><font color="Maroon">f</font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>

<a NAME="E3:34"/><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<a NAME="E4:34"/>
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10">incl</a> <font color="Maroon">C</font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10">incl</a> <font color="Maroon">C</font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">b</font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
<b>by </b><i><a class="ref" href="functor0.html#T29">FUNCTOR0:29</a></i>;<br/>
<a NAME="E5:34"/><b>then </b>
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10">incl</a> <font color="Maroon">C</font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="functor0.html#K10">incl</a> <font color="Maroon">C</font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">b</font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="functor0.html#K10">incl</a> <font color="Maroon">C</font></span>)</span> <a href="functor0.html#K6">.</a> <font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><a href="functor0.html#K5">Morph-Map</a> <span class="p2">(<span class="default"><a href="functor0.html#K10">incl</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font>
<b>by </b><i>, <a class="ref" href="functor0.html#D16">FUNCTOR0:def 16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font>
<b>by </b><i>, <a class="txt" href="yellow20.html#E1:34"><i><font color="Green">E25</font></i></a>, <a class="ref" href="msualg_3.html#D1">MSUALG_3:def 1</a></i>
<br/>.= 
<font color="Maroon">f</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>
;<br/><br/>


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