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

<b>set </b><font color="Maroon">a</font> = <font color="Maroon">o</font>,<font color="Maroon">o</font> <a href="funct_2.html#K4">:-&gt;</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="altcat_1.html#K1">^&gt;</a></span>;<br/>
<a NAME="E1:51_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font> <a href="funct_2.html#K4">:-&gt;</a> <span class="p2"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="altcat_1.html#K1">^&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span></span><a href="mcart_1.html#K12">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">o</font>,<font color="Maroon">o</font> <a href="funct_2.html#K4">:-&gt;</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="altcat_1.html#K1">^&gt;</a></span> as    <a href="pboole.html#M1">ManySortedSet</a> of <span class="p1"><a href="mcart_1.html#K12">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span></span><a href="mcart_1.html#K12">:]</a></span> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<b>set </b><font color="Maroon">m</font> = <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K4">]</a></span> <a href="cat_1.html#K7">.--&gt;</a> <span class="p1">(<span class="default">the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">C</font> <a href="altcat_1.html#K4">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span>)</span>;<br/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K4">]</a></span> <a href="cat_1.html#K7">.--&gt;</a> <span class="p2">(<span class="default">the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">C</font> <a href="altcat_1.html#K4">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span>)</span></span>)</span> = 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>
<br/>.= 
<span class="p1"><a href="mcart_1.html#K13">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span></span><a href="mcart_1.html#K13">:]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T39">MCART_1:39</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon">m</font> = <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K4">]</a></span> <a href="cat_1.html#K7">.--&gt;</a> <span class="p1">(<span class="default">the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">C</font> <a href="altcat_1.html#K4">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span>)</span> as    <a href="pboole.html#M1">ManySortedSet</a> of <span class="p1"><a href="mcart_1.html#K13">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span></span><a href="mcart_1.html#K13">:]</a></span> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E5:51_1_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">a</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font> <a href="hidden.html#R1">=</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">o</font>,<font color="Maroon">o</font>
 
<b>by </b><i><a class="ref" href="altcat_1.html#T12">ALTCAT_1:12</a></i>;<br/>
<a NAME="E6:51_1_1"/>
<font color="Maroon">m</font> is    <a href="pboole.html#M3">ManySortedFunction</a> of <span class="p1"><a href="altcat_1.html#K3">{|</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">a</font></span><a href="altcat_1.html#K3">|}</a></span>,<span class="p1"><a href="altcat_1.html#K2">{|</a><span class="default"><font color="Maroon">a</font></span><a href="altcat_1.html#K2">|}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D18">PBOOLE:def 18</a><br/>

<b>assume </b><a NAME="E1:51_1_1_2"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="mcart_1.html#K13">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span></span><a href="mcart_1.html#K13">:]</a></span>
 ;<br/>

<a NAME="E2:51_1_1_2"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T39">MCART_1:39</a></i>;<br/>
<a NAME="E3:51_1_1_2"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K4">]</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:51_1_1_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<i><font color="Green">E21</font></i>: <span class="p1"><a href="altcat_1.html#K3">{|</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">a</font></span><a href="altcat_1.html#K3">|}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1"><a href="altcat_1.html#K3">{|</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">a</font></span><a href="altcat_1.html#K3">|}</a></span> <a href="multop_1.html#K1">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font>
<b>by </b><i>, <a class="ref" href="multop_1.html#D1">MULTOP_1:def 1</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default">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">o</font>,<font color="Maroon">o</font></span>)</span>,<span class="p2">(<span class="default">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">o</font>,<font color="Maroon">o</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i>, , <a class="ref" href="altcat_1.html#D6">ALTCAT_1:def 6</a></i>
;<br/>
<span class="p1"><a href="altcat_1.html#K2">{|</a><span class="default"><font color="Maroon">a</font></span><a href="altcat_1.html#K2">|}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1"><a href="altcat_1.html#K2">{|</a><span class="default"><font color="Maroon">a</font></span><a href="altcat_1.html#K2">|}</a></span> <a href="multop_1.html#K1">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font>
<b>by </b><i>, <a class="ref" href="multop_1.html#D1">MULTOP_1:def 1</a></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">o</font>,<font color="Maroon">o</font>
<b>by </b><i>, , <a class="ref" href="altcat_1.html#D5">ALTCAT_1:def 5</a></i>
;<br/>
<b>hence </b><a NAME="E7:51_1_1_2"/>
<font color="Maroon">m</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="altcat_1.html#K3">{|</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">a</font></span><a href="altcat_1.html#K3">|}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>,<span class="p1"><a href="altcat_1.html#K2">{|</a><span class="default"><font color="Maroon">a</font></span><a href="altcat_1.html#K2">|}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i>, , <a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">m</font> = <font color="Maroon">m</font> as   <a href="altcat_1.html#NM3">BinComp</a> of <font color="Maroon">a</font> ;<br/>
<b>set </b><font color="Maroon">D</font> =  <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #);<br/>
<a NAME="E8:51_1_1"/>
 <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #) is    <a href="altcat_2.html#M1" target="_self">SubCatStr</a> of <font color="Maroon">C</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_1_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:51_1_1_3"/>
the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #) <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D11" target="_self">ALTCAT_2:def 11</a><br/>

<b>thus </b><a NAME="E2:51_1_1_3"/>
the <a href="altcat_1.html#U1">Arrows</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #) <a href="altcat_2.html#R2" target="_self">cc=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_1_3_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:51_1_1_3_1"/>
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #),the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #)</span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D2" target="_self">ALTCAT_2:def 2</a><br/>

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E2:51_1_1_3_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #),the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #)</span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<a NAME="E3:51_1_1_3_1"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K1">]</a></span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T35">ZFMISC_1:35</a></i>;<br/>
<a NAME="E4:51_1_1_3_1"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:51_1_1_3_1"/>
the <a href="altcat_1.html#U1">Arrows</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #) <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:51_1_1_3"/>
<span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #),the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #),the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #)</span><a href="zfmisc_1.html#K3">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C</font></span><a href="zfmisc_1.html#K3">:]</a></span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_2.html#D2" target="_self">ALTCAT_2:def 2</a><br/>

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E4:51_1_1_3"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #),the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #),the <a href="struct_0.html#U1">carrier</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #)</span><a href="zfmisc_1.html#K3">:]</a></span>
 ;<br/>

<a NAME="E5:51_1_1_3"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T39">MCART_1:39</a></i>;<br/>
<a NAME="E6:51_1_1_3"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K4">]</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then </b>the <a href="altcat_1.html#U2">Comp</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #) <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">C</font> <a href="altcat_1.html#K4">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font>
<b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>
<br/>.= 
the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="multop_1.html#D1">MULTOP_1:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E8:51_1_1_3"/>
the <a href="altcat_1.html#U2">Comp</a> of <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #) <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a> the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">D</font> =  <a href="altcat_1.html#G2">AltCatStr</a>(# <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span>,<font color="Maroon">a</font>,<font color="Maroon">m</font> #) as  <a href="altcat_1.html#V6">strict</a>  <a href="altcat_2.html#M1" target="_self">SubCatStr</a> of <font color="Maroon">C</font> ;<br/>
<b>take </b>
<font color="Maroon">D</font>
;<br/>

<b>thus </b><a NAME="E10:51_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">o</font></span><a href="domain_1.html#K6">}</a></span> &amp; the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">o</font>,<font color="Maroon">o</font> <a href="funct_2.html#K4">:-&gt;</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="altcat_1.html#K1">^&gt;</a></span> &amp; the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="domain_1.html#K4">]</a></span> <a href="cat_1.html#K7">.--&gt;</a> <span class="p1">(<span class="default">the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">C</font> <a href="altcat_1.html#K4">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span>)</span> )
 ;<br/>


</div>
