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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">F<sub>2</sub></font>(<span class="p1">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span>);<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a<sub>1</sub></font> <a href="mcart_1.html#K1">`1</a> ,<font color="Maroon">a<sub>1</sub></font> <a href="mcart_1.html#K2">`2</a> ,<font color="Maroon">a<sub>2</sub></font>];<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>,<font color="Maroon">a<sub>3</sub></font>,<font color="Maroon">a<sub>4</sub></font>,<font color="Maroon">a<sub>5</sub></font>);<br/>
<b>consider </b><font color="Maroon">P</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E2:6_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>1</sub></font>()</span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>and </b><br/><a NAME="E3:6_1"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>1</sub></font>()</span><a href="zfmisc_1.html#K2">:]</a></span> holds <br/>for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">i</font>) &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font>,<font color="Olive">x</font>] ) )
 <b>from </b><i><a class="ref" href="card_3.html#S4">CARD_3:sch 4</a>();<br/></i>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">P</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>;<br/>
<div><i><font color="Green">E48</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:6_1_1"/>
( <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="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <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="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <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#R1">=</a> <font color="Maroon">P</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <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"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>1</sub></font>()</span><a href="zfmisc_1.html#K2">:]</a></span> )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><b>hence </b><a NAME="E2:6_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> iff ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font>] ) )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E49</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</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> ;<br/><b>assume </b><a NAME="E1:6_1_2"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>) &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">b</font>,<font color="Maroon">c</font>) )
 ;<br/><a NAME="E2:6_1_2"/><b>then </b>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">f</font>] &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>,<font color="Maroon">c</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">g</font>] )
 <b>by </b><i/>;<br/><a NAME="E3:6_1_2"/><b>then </b>
( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">f</font>,<font color="Maroon">g</font>) <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">c</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">f</font>,<font color="Maroon">g</font>)] )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:6_1_2"/>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">f</font>,<font color="Maroon">g</font>) <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">c</font>)
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E50</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</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><a NAME="E1:6_1_3"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>) &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">b</font>,<font color="Maroon">c</font>) &amp; <font color="Maroon">h</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c</font>,<font color="Maroon">d</font>) )
 ;<br/><a NAME="E2:6_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">f</font>] &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>,<font color="Maroon">c</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">g</font>] &amp; <font color="Maroon">h</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c</font>,<font color="Maroon">d</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">h</font>] )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:6_1_3"/>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">f</font>,<font color="Maroon">g</font>),<font color="Maroon">h</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">d</font>,<font color="Maroon">f</font>,<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">g</font>,<font color="Maroon">h</font>))
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E53</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>consider </b><font color="Maroon">f</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:6_1_4"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">a</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">a</font>,<font color="Maroon">f</font>] )
 <b>and </b><br/><a NAME="E3:6_1_4"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<br/> for <font color="Olive">g</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Olive">b</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Olive">b</font>,<font color="Olive">g</font>] holds <br/><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">a</font>,<font color="Olive">b</font>,<font color="Maroon">f</font>,<font color="Olive">g</font>) <a href="hidden.html#R1">=</a> <font color="Olive">g</font>
 <b>by </b><i/>;<br/><b>take </b><font color="Maroon">f</font> = <font color="Maroon">f</font>;<br/><b>thus </b><a NAME="E4:6_1_4"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">a</font>)
 <b>by </b><i>, </i>;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">g</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E5:6_1_4"/>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>)
 ;<br/><a NAME="E6:6_1_4"/><b>then </b>
( <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">g</font>] )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E7:6_1_4"/>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">f</font>,<font color="Maroon">g</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E56</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>consider </b><font color="Maroon">f</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:6_1_5"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">a</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">a</font>,<font color="Maroon">f</font>] )
 <b>and </b><br/><a NAME="E3:6_1_5"/><i><font color="Green">E62</font></i>: 
for <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<br/> for <font color="Olive">g</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b</font>,<font color="Maroon">a</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b</font>,<font color="Maroon">a</font>,<font color="Olive">g</font>] holds <br/><font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b</font>,<font color="Maroon">a</font>,<font color="Maroon">a</font>,<font color="Olive">g</font>,<font color="Maroon">f</font>) <a href="hidden.html#R1">=</a> <font color="Olive">g</font>
 <b>by </b><i/>;<br/><b>take </b><font color="Maroon">f</font> = <font color="Maroon">f</font>;<br/><b>thus </b><a NAME="E4:6_1_5"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">a</font>)
 <b>by </b><i>, </i>;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">g</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E5:6_1_5"/>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">b</font>,<font color="Maroon">a</font>)
 ;<br/><a NAME="E6:6_1_5"/><b>then </b>
( <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>,<font color="Maroon">a</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">g</font>] )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E7:6_1_5"/>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">a</font>,<font color="Maroon">g</font>,<font color="Maroon">f</font>) <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">C</font> being  <a href="altcat_1.html#V6">strict</a> <a href="altcat_1.html#NM4">category</a><b> such that </b><br/><a NAME="E10:6_1"/><i><font color="Green">E66</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E11:6_1"/><i><font color="Green">E67</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font> holds  <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">a</font>,<font color="Olive">b</font>)
 <b>and </b><br/><a NAME="E12:6_1"/><i><font color="Green">E68</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font>  st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">a</font>,<font color="Olive">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>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b</font>,<font color="Olive">c</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>  holds <br/>for <font color="Olive">f</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font><br/> for <font color="Olive">g</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b</font>,<font color="Olive">c</font> holds  <font color="Olive">g</font> <a href="altcat_1.html#K5">*</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">c</font>,<font color="Olive">f</font>,<font color="Olive">g</font>)
 <b>from </b><i><a class="ref" href="yellow18.html#S4" target="_self">YELLOW18:sch 4</a>(, , , );<br/></i>
<b>take </b>
<font color="Maroon">C</font>
;<br/>

<b>thus </b><a NAME="E13:6_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>by </b><i/>;<br/>

<div><b>hereby </b>
<div class="add"><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>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:6_1_6"/>
<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#R1">=</a> <font color="Maroon">P</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:6_1_6"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <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> iff ( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">f</font>] ) )
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E15:6_1"/>
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font>  st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">a</font>,<font color="Olive">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>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b</font>,<font color="Olive">c</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>  holds <br/>for <font color="Olive">f</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font><br/> for <font color="Olive">g</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b</font>,<font color="Olive">c</font> holds  <font color="Olive">g</font> <a href="altcat_1.html#K5">*</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">c</font>,<font color="Olive">f</font>,<font color="Olive">g</font>)
 <b>by </b><i/>;<br/>


</div>
