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<b>let </b><font color="Maroon">i</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">j</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">k</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">l</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">alt</font> = <font color="Maroon">F<sub>1</sub></font>();<br/>
<b>set </b><font color="Maroon">IT</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">B</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">i'</font> = <font color="Maroon">i</font>, <font color="Maroon">j'</font> = <font color="Maroon">j</font>, <font color="Maroon">k'</font> = <font color="Maroon">k</font>, <font color="Maroon">l'</font> = <font color="Maroon">l</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">f</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">h</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">E39</font></i>: 
<font color="Maroon">f</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">i</font>,<font color="Maroon">j</font>
 <b>and </b><br/><a NAME="E3:2_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">g</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">j</font>,<font color="Maroon">k</font>
 <b>and </b><br/><a NAME="E4:2_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">h</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">k</font>,<font color="Maroon">l</font>
 ;<br/>

<a NAME="E5:2_1"/><i><font color="Green">E48</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">i</font>,<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">i'</font>,<font color="Maroon">j'</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
;<br/>
<b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">i'</font>,<font color="Maroon">j'</font> <b>by </b><i/>;<br/>
<a NAME="E7:2_1"/><i><font color="Green">E49</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">j</font>,<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">j'</font>,<font color="Maroon">k'</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
;<br/>
<b>reconsider </b><font color="Maroon">g'</font> = <font color="Maroon">g</font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">j'</font>,<font color="Maroon">k'</font> <b>by </b><i/>;<br/>
<a NAME="E9:2_1"/><i><font color="Green">E50</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">k</font>,<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">k'</font>,<font color="Maroon">l'</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
;<br/>
<b>reconsider </b><font color="Maroon">h'</font> = <font color="Maroon">h</font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">k'</font>,<font color="Maroon">l'</font> <b>by </b><i/>;<br/>
<a NAME="E11:2_1"/><i><font color="Green">E53</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">i'</font>,<font color="Maroon">k'</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">j'</font>,<font color="Maroon">l'</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>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">i</font>,<font color="Maroon">k</font>,<font color="Maroon">l</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">h</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">i</font>,<font color="Maroon">j</font>,<font color="Maroon">k</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">g</font>,<font color="Maroon">f</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">i</font>,<font color="Maroon">k</font>,<font color="Maroon">l</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">h</font>,<span class="p1">(<span class="default"><font color="Maroon">g'</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">f'</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="altcat_1.html#D10">ALTCAT_1:def 10</a></i>
<br/>.= 
<font color="Maroon">h'</font> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">g'</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">f'</font></span>)</span>
<b>by </b><i>, , <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">i</font>,<font color="Maroon">k</font>,<font color="Maroon">l</font>,<span class="p1">(<span class="default"><font color="Maroon">g'</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">f'</font></span>)</span>,<font color="Maroon">h'</font>)
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">i</font>,<font color="Maroon">k</font>,<font color="Maroon">l</font>,<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">i</font>,<font color="Maroon">j</font>,<font color="Maroon">k</font>,<font color="Maroon">f</font>,<font color="Maroon">g</font>),<font color="Maroon">h</font>)
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">i'</font>,<font color="Maroon">j'</font>,<font color="Maroon">l'</font>,<font color="Maroon">f</font>,<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">j'</font>,<font color="Maroon">k'</font>,<font color="Maroon">l'</font>,<font color="Maroon">g</font>,<font color="Maroon">h</font>))
<b>by </b><i>, , , , , , </i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">i'</font>,<font color="Maroon">j'</font>,<font color="Maroon">l'</font>,<font color="Maroon">f</font>,<span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">g'</font></span>)</span>)
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">g'</font></span>)</span> <a href="altcat_1.html#K5">*</a> <font color="Maroon">f'</font>
<b>by </b><i>, , </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">i</font>,<font color="Maroon">j</font>,<font color="Maroon">l</font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">g'</font></span>)</span>,<font color="Maroon">f</font>
<b>by </b><i>, , <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">i</font>,<font color="Maroon">j</font>,<font color="Maroon">l</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">j</font>,<font color="Maroon">k</font>,<font color="Maroon">l</font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">h</font>,<font color="Maroon">g</font></span>)</span>,<font color="Maroon">f</font>
<b>by </b><i>, , <a class="ref" href="altcat_1.html#D10">ALTCAT_1:def 10</a></i>
;<br/>


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