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<b>let </b><font color="Maroon">A</font> be  <a href="altcat_1.html#V9">semi-functional</a> <a href="yellow18.html#V2">para-functional</a> <a href="altcat_1.html#NM4">category</a>, <font color="Maroon">B</font> be  <a href="altcat_1.html#V9">semi-functional</a> <a href="yellow18.html#V2">para-functional</a> <a href="altcat_1.html#NM4">category</a>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a1</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>, <font color="Maroon">a2</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>, <font color="Maroon">a3</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>;<br/><b>assume </b><a NAME="E1:13_1"/><i><font color="Green">E25</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</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>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a2</font>,<font color="Maroon">a3</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">b1</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font>, <font color="Maroon">b2</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font>, <font color="Maroon">b3</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font>;<br/><b>assume </b><b>that </b><br/><a NAME="E2:13_1"/><i><font color="Green">E32</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</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>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">b2</font>,<font color="Maroon">b3</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>  )
 <b>and </b><br/><a NAME="E3:13_1"/>
( <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a1</font> &amp; <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">b3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font> )
 ;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">a1</font>,<font color="Maroon">a2</font>;<br/><b>let </b><font color="Maroon">g1</font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">b1</font>,<font color="Maroon">b2</font>;<br/><b>assume </b><a NAME="E4:13_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">g1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font>
 ;<br/><b>let </b><font color="Maroon">f2</font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">a2</font>,<font color="Maroon">a3</font>;<br/><b>let </b><font color="Maroon">g2</font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">b2</font>,<font color="Maroon">b3</font>;<br/><b>assume </b><a NAME="E5:13_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">g2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 ;<br/><b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f1</font> as   <a href="funct_2.html#NM1">Function</a> of  <a href="yellow18.html#K3">the_carrier_of</a> <font color="Maroon">a1</font>, <a href="yellow18.html#K3">the_carrier_of</a> <font color="Maroon">a2</font> <b>by </b><i>, <a class="ref" href="yellow18.html#T35">YELLOW18:35</a></i>;<br/><b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f2</font> as   <a href="funct_2.html#NM1">Function</a> of  <a href="yellow18.html#K3">the_carrier_of</a> <font color="Maroon">a2</font>, <a href="yellow18.html#K3">the_carrier_of</a> <font color="Maroon">a3</font> <b>by </b><i>, <a class="ref" href="yellow18.html#T35">YELLOW18:35</a></i>;<br/><a NAME="E8:13_1"/><i><font color="Green">E39</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a3</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>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b3</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>  )
 <b>by </b><i>, , <a class="ref" href="altcat_1.html#D4">ALTCAT_1:def 4</a></i>;<br/><b>hence </b><font color="Maroon">f2</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">f1</font> = 
<font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>
<b>by </b><i>, <a class="ref" href="altcat_1.html#D14">ALTCAT_1:def 14</a></i>
<br/>.= 
<font color="Maroon">g2</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">g1</font>
<b>by </b><i>, , , , <a class="ref" href="altcat_1.html#D14">ALTCAT_1:def 14</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:13"/>
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="yellow20.html#R1" target="_self">have_the_same_composition</a> 
 <b>by </b><i/>;<br/>


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