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

<b>set </b><font color="Maroon">A</font> = <font color="Maroon">F<sub>1</sub></font>();<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> ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="tarski.html#K4">]</a></span> &amp; ( for <font color="Olive">f</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a<sub>2</sub></font> iff ( <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">a</font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">f</font>] ) ) ) );<br/>
<div><i><font color="Green">E39</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:76_1_1"/>
<font color="Maroon">x</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>
 ;<br/><b>then consider </b><font color="Maroon">a</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:76_1_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">x</font> <a href="hidden.html#R1">=</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> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/><b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">a<sub>1</sub></font>];<br/><b>consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:76_1_1"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">f</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> iff ( <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>) &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">f</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i><b>take </b><font color="Maroon">y</font> = <font color="Maroon">y</font>;<br/><b>thus </b><a NAME="E6:76_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">x</font>,<font color="Maroon">y</font>]
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">F</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E3:76_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</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="E4:76_1"/><i><font color="Green">E48</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</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/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>]
 <b>from </b><i><a class="ref" href="zfrefle1.html#S1">ZFREFLE1:sch 1</a>(<a class="txt" href="yellow18.html#E1:76_1"><i><font color="Green">E39</font></i></a>);<br/></i>
<div><i><font color="Green">E49</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:76_1_2"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() )
 ;<br/><a NAME="E2:76_1_2"/><b>then </b>
<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="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>then consider </b><font color="Maroon">a'</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">b'</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:76_1_2"/><i><font color="Green">E50</font></i>: 
<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> <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>
 <b>and </b><br/><a NAME="E5:76_1_2"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">f</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</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> iff ( <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a'</font>),<font color="Maroon">F<sub>2</sub></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="Olive">f</font>] ) )
 <b>by </b><i/>;<br/><a NAME="E6:76_1_2"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b'</font> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>thus </b><a NAME="E7:76_1_2"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</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> iff ( <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">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>) ) )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>deffunc </b><font color="Maroon">H<sub>1</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">F</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>;<br/>
<div><i><font color="Green">E55</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="76_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>();<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>assume </b><a NAME="E1:76_1_3"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>1</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>1</sub></font>(<font color="Maroon">b</font>,<font color="Maroon">c</font>) )
 ;<br/><a NAME="E2:76_1_3"/><b>then </b><i><font color="Green">E56</font></i>: 
( <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">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</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">g</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c</font>) )
 <b>by </b><i/>;<br/><a NAME="E3:76_1_3"/><b>then </b>
(  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>) &amp;  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>) &amp;  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>) &amp;  <a href="funct_5.html#K2">proj2</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c</font>) )
 <b>by </b><i/>;<br/><a NAME="E4:76_1_3"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>) &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>) &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>) &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c</font>) &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g</font> )
 <b>by </b><i><a class="ref" href="funct_5.html#T21">FUNCT_5:21</a>, <a class="ref" href="relat_1.html#T45">RELAT_1:45</a></i>;<br/><a NAME="E5:76_1_3"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>) &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c</font>) )
 <b>by </b><i><a class="ref" href="relat_1.html#T46">RELAT_1:46</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><a NAME="E6:76_1_3"/><b>then </b>
( <font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>),<font color="Maroon">F<sub>2</sub></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">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font>] )
 <b>by </b><i>, , <a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/><b>hence </b><a NAME="E7:76_1_3"/>
<font color="Maroon">g</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>1</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">E58</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="76_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>(), <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>thus </b><a NAME="E1:76_1_4"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>) <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>)
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>thus </b><a NAME="E1:76_1_4_1"/>
(  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">b</font>) or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">b</font>) )
 <b>by </b><i/>;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<a NAME="E8:76_1"/><i><font color="Green">E62</font></i>: 
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds   <a href="partfun1.html#K6">id</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">a</font>) <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">a</font>,<font color="Olive">a</font>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_5"><b>proof </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/>

<a NAME="E1:76_1_5"/>
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>)</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>) &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>)</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>) )
 
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<a NAME="E2:76_1_5"/><b>then </b>
( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">a</font>, <a href="partfun1.html#K6">id</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>)] &amp;  <a href="partfun1.html#K6">id</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>) <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>) )
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D2">FUNCT_2:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:76_1_5"/>
 <a href="partfun1.html#K6">id</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>) <a href="hidden.html#R2">in</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">a</font>,<font color="Maroon">a</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#V9">semi-functional</a> <a href="yellow18.html#V2" target="_self">para-functional</a> <a href="yellow18.html#V3" target="_self">set-id-inheriting</a> <a href="altcat_1.html#NM4">category</a><b> such that </b><br/><a NAME="E10:76_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="E11:76_1"/><i><font color="Green">E67</font></i>: 
for <font color="Olive">a</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font> holds   <a href="yellow18.html#K3" target="_self">the_carrier_of</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">a</font>)
 <b>and </b><br/><a NAME="E12:76_1"/><i><font color="Green">E68</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>1</sub></font>(<font color="Olive">a</font>,<font color="Olive">b</font>)
 <b>from </b><i><a class="ref" href="yellow18.html#S16" target="_self">YELLOW18:sch 16</a>(, , );<br/></i>
<b>take </b>
<font color="Maroon">C</font>
;<br/>

<b>thus </b><a NAME="E13:76_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/>

<b>thus </b><a NAME="E14:76_1"/>
for <font color="Olive">a</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font> holds   <a href="yellow18.html#K3" target="_self">the_carrier_of</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">a</font>)
 <b>by </b><i/>;<br/>

<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">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a</font>, <font color="Maroon">b</font> = <font color="Maroon">b</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font> <b>by </b><i/>;<br/>
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> = 
<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>

<br/>.= 
<font color="Maroon">F</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>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E17:76_1"/>
( <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">C</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> iff ( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a</font>),<font color="Maroon">F<sub>2</sub></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/>;<br/>


</div>
