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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:13_1"/><i><font color="Green">E9</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></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">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>assume </b><b>that </b><br/><a NAME="E2:13_1"/><i><font color="Green">E10</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></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">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></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">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/><b>assume </b><a NAME="E4:13_1"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>12</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/><b>assume </b><a NAME="E5:13_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="funct_2.html#NM1">Function</a> of  <a href="yellow18.html#K3">the_carrier_of</a> <font color="Maroon">c<sub>3</sub></font>, <a href="yellow18.html#K3">the_carrier_of</a> <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="yellow20.html#E1:13_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="yellow18.html#T35">YELLOW18:35</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>11</sub></font> as   <a href="funct_2.html#NM1">Function</a> of  <a href="yellow18.html#K3">the_carrier_of</a> <font color="Maroon">c<sub>4</sub></font>, <a href="yellow18.html#K3">the_carrier_of</a> <font color="Maroon">c<sub>5</sub></font> <b>by </b><i><a class="txt" href="yellow20.html#E1:13_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="yellow18.html#T35">YELLOW18:35</a></i>;<br/><a NAME="E8:13_1"/><i><font color="Green">E13</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></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="txt" href="yellow20.html#E1:13_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="yellow20.html#E2:13_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="altcat_1.html#D4">ALTCAT_1:def 4</a></i>;<br/><b>hence </b><font color="Maroon">c<sub>11</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>9</sub></font> = 
<font color="Maroon">c<sub>14</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="yellow20.html#E1:13_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="altcat_1.html#D14">ALTCAT_1:def 14</a></i>
<br/>.= 
<font color="Maroon">c<sub>12</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="yellow20.html#E2:13_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="yellow20.html#E4:13_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="yellow20.html#E5:13_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="yellow20.html#E8:13_1"><i><font color="Green">E13</font></i></a>, <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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="yellow20.html#R1" target="_self">have_the_same_composition</a> 
 <b>by </b><i><a class="ref" href="yellow20.html#T11" target="_self">Th11</a></i>;<br/>


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