<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(); <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_1.html#D7">ALTCAT_1:def 7</a>,<a class="ref" href="altcat_1.html#D17">ALTCAT_1:def 17</a><br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">F<sub>1</sub></font>();<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>() ;<br/>
<b>let </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:2_1"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E3:2_1"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E4:2_1"/><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E5:2_1"/><i><font color="Green">E6</font></i>: 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
;<br/>
<b>reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>12</sub></font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font> <b>by </b><i><a class="txt" href="yellow18.html#E2:2_1"><i><font color="Green">E3</font></i></a></i>;<br/>
<a NAME="E7:2_1"/><i><font color="Green">E7</font></i>: 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
;<br/>
<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>13</sub></font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font> <b>by </b><i><a class="txt" href="yellow18.html#E3:2_1"><i><font color="Green">E4</font></i></a></i>;<br/>
<a NAME="E9:2_1"/><i><font color="Green">E8</font></i>: 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
;<br/>
<b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>14</sub></font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <b>by </b><i><a class="txt" href="yellow18.html#E4:2_1"><i><font color="Green">E5</font></i></a></i>;<br/>
<a NAME="E11:2_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>8</sub></font>,<font color="Maroon">c<sub>10</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>9</sub></font>,<font color="Maroon">c<sub>11</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="yellow18.html#E2:2_1"><i><font color="Green">E3</font></i></a>, <a class="txt" href="yellow18.html#E3:2_1"><i><font color="Green">E4</font></i></a>, <a class="txt" href="yellow18.html#E4:2_1"><i><font color="Green">E5</font></i></a>, <a class="txt" href="yellow18.html#E5:2_1"><i><font color="Green">E6</font></i></a>, <a class="txt" href="yellow18.html#E7:2_1"><i><font color="Green">E7</font></i></a>, <a class="txt" href="yellow18.html#E9:2_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="altcat_1.html#D4">ALTCAT_1:def 4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default">the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="altcat_1.html#K4">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="altcat_1.html#K4">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> = 
<span class="p1">(<span class="default">the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="altcat_1.html#K4">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="yellow18.html#E2:2_1"><i><font color="Green">E3</font></i></a>, <a class="txt" href="yellow18.html#E3:2_1"><i><font color="Green">E4</font></i></a>, <a class="ref" href="altcat_1.html#D10">ALTCAT_1:def 10</a></i>
<br/>.= 
<font color="Maroon">c<sub>17</sub></font> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="yellow18.html#E4:2_1"><i><font color="Green">E5</font></i></a>, <a class="txt" href="yellow18.html#E11:2_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="altcat_1.html#D10">ALTCAT_1:def 10</a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>,<font color="Maroon">c<sub>17</sub></font>)
<b>by </b><i><a class="txt" href="yellow18.html#E1:2"><i><font color="Green">E1</font></i></a>, <a class="txt" href="yellow18.html#E4:2_1"><i><font color="Green">E5</font></i></a>, <a class="txt" href="yellow18.html#E11:2_1"><i><font color="Green">E9</font></i></a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>),<font color="Maroon">c<sub>14</sub></font>)
<b>by </b><i><a class="txt" href="yellow18.html#E1:2"><i><font color="Green">E1</font></i></a>, <a class="txt" href="yellow18.html#E2:2_1"><i><font color="Green">E3</font></i></a>, <a class="txt" href="yellow18.html#E3:2_1"><i><font color="Green">E4</font></i></a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font>))
<b>by </b><i><a class="txt" href="yellow18.html#E2:2"><i><font color="Green">E2</font></i></a>, <a class="txt" href="yellow18.html#E2:2_1"><i><font color="Green">E3</font></i></a>, <a class="txt" href="yellow18.html#E3:2_1"><i><font color="Green">E4</font></i></a>, <a class="txt" href="yellow18.html#E4:2_1"><i><font color="Green">E5</font></i></a>, <a class="txt" href="yellow18.html#E5:2_1"><i><font color="Green">E6</font></i></a>, <a class="txt" href="yellow18.html#E7:2_1"><i><font color="Green">E7</font></i></a>, <a class="txt" href="yellow18.html#E9:2_1"><i><font color="Green">E8</font></i></a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span>)
<b>by </b><i><a class="txt" href="yellow18.html#E1:2"><i><font color="Green">E1</font></i></a>, <a class="txt" href="yellow18.html#E3:2_1"><i><font color="Green">E4</font></i></a>, <a class="txt" href="yellow18.html#E4:2_1"><i><font color="Green">E5</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="yellow18.html#E1:2"><i><font color="Green">E1</font></i></a>, <a class="txt" href="yellow18.html#E2:2_1"><i><font color="Green">E3</font></i></a>, <a class="txt" href="yellow18.html#E11:2_1"><i><font color="Green">E9</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="altcat_1.html#K4">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>16</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="yellow18.html#E2:2_1"><i><font color="Green">E3</font></i></a>, <a class="txt" href="yellow18.html#E11:2_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="altcat_1.html#D10">ALTCAT_1:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="altcat_1.html#K4">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="altcat_1.html#K4">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font></span>)</span>,<font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="yellow18.html#E3:2_1"><i><font color="Green">E4</font></i></a>, <a class="txt" href="yellow18.html#E4:2_1"><i><font color="Green">E5</font></i></a>, <a class="ref" href="altcat_1.html#D10">ALTCAT_1:def 10</a></i>
;<br/>


</div>
