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

<b>set </b><font color="Maroon" title="c1">A</font> = <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c2">B</font> = <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c3">C</font> = <span class="p1"><a href="mcart_1.html#K13" title="MCART_1:func.13">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p2"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span></span><a href="mcart_1.html#K13" title="MCART_1:func.13">:]</a></span>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">b0</font> = 0, <font color="Maroon" title="c5">b1</font> = 1 as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">h</font> = 0, <font color="Maroon" title="c7">R</font> = 1 as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">p0</font> = 0, <font color="Maroon" title="c9">p1</font> = 1, <font color="Maroon" title="c10">p2</font> = 2, <font color="Maroon" title="c11">p3</font> = 3 as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3 <b>by </b><i><a class="ref" href="turing_1.html#T1" target="_self" title="TURING_1:th.1">Th1</a></i>;<br/>
<a NAME="E4:70_1_1"/>
<span class="p1"><a href="mcart_1.html#K13" title="MCART_1:func.13">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p2"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span></span><a href="mcart_1.html#K13" title="MCART_1:func.13">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p3">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p3"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<span class="p2"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D3" title="ZFMISC_1:def.3">ZFMISC_1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c12">OP</font> =  <a href="turing_1.html#K12" title="TURING_1:func.12">id</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>,<font color="Maroon" title="c6">h</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<span class="p1"><a href="mcart_1.html#K13" title="MCART_1:func.13">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p2"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span></span><a href="mcart_1.html#K13" title="MCART_1:func.13">:]</a></span> ;<br/>
<a NAME="E6:70_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K12" title="TURING_1:func.12">id</a> <span class="p0"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p1">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<span class="p0"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>,0</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><span class="p0"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p0"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,0,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><span class="p5"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,1</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,0,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">2,0,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,1</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">2,0,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">3,0,0</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c12">OP</font> <a href="turing_1.html#K1" title="TURING_1:func.1">+*</a> <span class="p5">(<span class="default"><span class="p0"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">p0</font>,<font color="Maroon" title="c4">b0</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p0"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c4">b0</font>,<font color="Maroon" title="c7">R</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="turing_1.html#K1" title="TURING_1:func.1">+*</a> <span class="p4">(<span class="default"><span class="p5"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c5">b1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c4">b0</font>,<font color="Maroon" title="c7">R</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="turing_1.html#K1" title="TURING_1:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c4">b0</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c10">p2</font>,<font color="Maroon" title="c4">b0</font>,<font color="Maroon" title="c7">R</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="turing_1.html#K1" title="TURING_1:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c10">p2</font>,<font color="Maroon" title="c5">b1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c10">p2</font>,<font color="Maroon" title="c4">b0</font>,<font color="Maroon" title="c7">R</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="turing_1.html#K1" title="TURING_1:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c10">p2</font>,<font color="Maroon" title="c4">b0</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><font color="Maroon" title="c11">p3</font>,<font color="Maroon" title="c4">b0</font>,<font color="Maroon" title="c6">h</font></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E7:70_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="turing_1.html#K12" title="TURING_1:func.12">id</a> <span class="p0"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p1">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<span class="p0"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>,0</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><span class="p0"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">0,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p0"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,0,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><span class="p5"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,1</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p5"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">1,0,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><span class="p4"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">1,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p4"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">2,0,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,1</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p3"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">2,0,1</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,0</span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="turing_1.html#K2" title="TURING_1:func.2">.--&gt;</a> <span class="p2"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default">3,0,0</span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span></span>)</span> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>,<span class="p1"><a href="mcart_1.html#K13" title="MCART_1:func.13">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K3" title="TURING_1:func.3">SegM</a> 3</span>)</span>,<span class="p2"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p2"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span></span><a href="mcart_1.html#K13" title="MCART_1:func.13">:]</a></span>
 ;<br/>


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