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

<b>set </b><font color="Maroon">c<sub>1</sub></font> = <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span>;<br/>
<a NAME="E1:11_2_1"/><i><font color="Green">E10</font></i>: 
 <a href="yellow_1.html#K2">InclPoset</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span> is <a href="lattice3.html#V1">with_suprema</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:11_2_1_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span> )
 ;<br/><a NAME="E2:11_2_1_1_1"/><b>then </b><i><font color="Green">E11</font></i>: 
( ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 ) &amp; ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 ) )
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><i><font color="Green">E12</font></i>: <span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span> <a href="xboole_0.html#K2">\/</a> 2 = 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default">0,1,1,2</span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="enumset1.html#T45">ENUMSET1:45</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default">1,1,0,2</span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T110">ENUMSET1:110</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,0,2</span><a href="enumset1.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T71">ENUMSET1:71</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default">0,1,2</span><a href="enumset1.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T99">ENUMSET1:99</a></i>
;<br/><a NAME="E4:11_2_1_1_1"/><i><font color="Green">E13</font></i>: 
<span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">1,2</span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="ref" href="zfmisc_1.html#T14">ZFMISC_1:14</a></i>;<br/><a NAME="E5:11_2_1_1_1"/><i><font color="Green">E14</font></i>: 
<span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span> <a href="xboole_0.html#K2">\/</a> 3 <a href="hidden.html#R1">=</a> 3
 <b>by </b><i><a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>;<br/><a NAME="E6:11_2_1_1_1"/><i><font color="Green">E15</font></i>: 
( 2 <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span> <a href="hidden.html#R1">=</a> 2 <a href="xboole_0.html#K2">\/</a> 3 &amp; 2 <a href="tarski.html#R1">c=</a> 3 )
 <b>by </b><i><a class="ref" href="card_1.html#T56">CARD_1:56</a>, <a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>;<br/><a NAME="E7:11_2_1_1_1"/><b>then </b><i><font color="Green">E16</font></i>: 
2 <a href="xboole_0.html#K2">\/</a> 3 <a href="hidden.html#R1">=</a> 3
 <b>by </b><i><a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>;<br/><a NAME="E8:11_2_1_1_1"/>
<span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span> <a href="xboole_0.html#K2">\/</a> 3 <a href="hidden.html#R1">=</a> 3
 <b>by </b><i><a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>;<br/><b>hence </b><a NAME="E9:11_2_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:11_2_1_1_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="yellow11.html#E3:11_2_1_1_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="yellow11.html#E4:11_2_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="yellow11.html#E5:11_2_1_1_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="yellow11.html#E6:11_2_1_1_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="yellow11.html#E7:11_2_1_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:11_2_1_1"/>
 <a href="yellow_1.html#K2">InclPoset</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span> is <a href="lattice3.html#V1">with_suprema</a>
 <b>by </b><i><a class="ref" href="yellow_1.html#T11">YELLOW_1:11</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:11_2_1"/>
 <a href="yellow_1.html#K2">InclPoset</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span> is <a href="lattice3.html#V2">with_infima</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D11">LATTICE3:def 11</a><br/>

<a NAME="E1:11_2_1_2"/><i><font color="Green">E11</font></i>: 
<span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/>
<b>thus </b><a NAME="E2:11_2_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> st <font color="Olive">b<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>1</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:11_2_1_2_1_1"/>
( ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 ) )
 </span><b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2"><i><font color="Green">E11</font></i></a>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_1"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_2"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_2"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_2"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_3"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_3"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_3"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_3"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_3"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_3"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_3"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_4"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_4"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_4"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_4"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_4"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_4"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_4"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_4"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_5"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_5"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_5"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_5"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_5"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_5"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_5"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_5"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_6"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_6"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_6"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_6"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_6"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_6"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_6"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_6"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_7"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_7"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_7"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_7"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_7"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_7"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_7"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_7"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_8"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_8"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 )
 ;<br/><div class="add"><a NAME="E2:11_2_1_2_1_1_8"/>
0 <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = 0 as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E4:11_2_1_2_1_1_8"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/><b>hence </b><a NAME="E5:11_2_1_2_1_1_8"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><a NAME="E6:11_2_1_2_1_1_8"/>
<font color="Maroon">c<sub>6</sub></font> is    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span>
 <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_8"/><b>then </b><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3 )
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>assume </b><a NAME="E8:11_2_1_2_1_1_8"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E9:11_2_1_2_1_1_8"/><b>then </b><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> 2 )
 <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2_1_1_8"><i><font color="Green">E12</font></i></a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><div><i><font color="Green">E15</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2_1_1_8_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_2_1_1_8_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1
 ;<br/><a NAME="E2:11_2_1_2_1_1_8_1"/><b>then </b>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; not 2 <a href="hidden.html#R2">in</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E3:11_2_1_2_1_1_8_1"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E9:11_2_1_2_1_1_8"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E16</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2_1_1_8_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_2_1_1_8_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><a NAME="E2:11_2_1_2_1_1_8_2"/><b>then </b>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; not 0 <a href="hidden.html#R2">in</a> 3 <a href="subset_1.html#K6">\</a> 1 )
 <b>by </b><i><a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E3:11_2_1_2_1_1_8_2"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E9:11_2_1_2_1_1_8"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2_1_1_8_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_2_1_1_8_3"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2
 ;<br/><a NAME="E2:11_2_1_2_1_1_8_3"/><b>then </b>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; not 2 <a href="hidden.html#R2">in</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:11_2_1_2_1_1_8_3"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E9:11_2_1_2_1_1_8"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2_1_1_8_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_2_1_1_8_4"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3
 ;<br/><a NAME="E2:11_2_1_2_1_1_8_4"/><b>then </b>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; not 2 <a href="hidden.html#R2">in</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:11_2_1_2_1_1_8_4"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E9:11_2_1_2_1_1_8"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E14:11_2_1_2_1_1_8"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="yellow11.html#E7:11_2_1_2_1_1_8"><i><font color="Green">E13</font></i></a>, <a class="txt" href="yellow11.html#E10:11_2_1_2_1_1_8"><i><font color="Green">E15</font></i></a>, <a class="txt" href="yellow11.html#E11:11_2_1_2_1_1_8"><i><font color="Green">E16</font></i></a>, <a class="txt" href="yellow11.html#E12:11_2_1_2_1_1_8"><i><font color="Green">E17</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_9"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_9"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="ref" href="zfmisc_1.html#T19">ZFMISC_1:19</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_9"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_9"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_9"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_9"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_9"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_9"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_10"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_10"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 )
 ;<br/><div class="add"><span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span> <a href="subset_1.html#K8">/\</a> 3 = 
<span class="p1">(<span class="default">3 <a href="xboole_0.html#K3">/\</a> 3</span>)</span> <a href="subset_1.html#K6">\</a> 1
<b>by </b><i><a class="ref" href="xboole_1.html#T49">XBOOLE_1:49</a></i>
<br/>.= 
3 <a href="subset_1.html#K6">\</a> 1

;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2_1_1_10"><i><font color="Green">E12</font></i></a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E4:11_2_1_2_1_1_10"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E5:11_2_1_2_1_1_10"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E6:11_2_1_2_1_1_10"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E7:11_2_1_2_1_1_10"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E8:11_2_1_2_1_1_10"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E9:11_2_1_2_1_1_10"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_11"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_11"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_11"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_11"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_11"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_11"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_11"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_11"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_12"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_12"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 )
 ;<br/><div class="add"><a NAME="E2:11_2_1_2_1_1_12"/>
0 <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = 0 as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E4:11_2_1_2_1_1_12"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/><b>hence </b><a NAME="E5:11_2_1_2_1_1_12"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><a NAME="E6:11_2_1_2_1_1_12"/>
<font color="Maroon">c<sub>6</sub></font> is    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span>
 <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_12"/><b>then </b><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3 )
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>assume </b><a NAME="E8:11_2_1_2_1_1_12"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E9:11_2_1_2_1_1_12"/><b>then </b><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> 3 <a href="subset_1.html#K6">\</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> 2 )
 <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2_1_1_12"><i><font color="Green">E12</font></i></a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><div><i><font color="Green">E15</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2_1_1_12_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_2_1_1_12_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1
 ;<br/><a NAME="E2:11_2_1_2_1_1_12_1"/><b>then </b>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; not 2 <a href="hidden.html#R2">in</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E3:11_2_1_2_1_1_12_1"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E9:11_2_1_2_1_1_12"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E16</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2_1_1_12_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_2_1_1_12_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><a NAME="E2:11_2_1_2_1_1_12_2"/><b>then </b>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; not 0 <a href="hidden.html#R2">in</a> 3 <a href="subset_1.html#K6">\</a> 1 )
 <b>by </b><i><a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E3:11_2_1_2_1_1_12_2"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E9:11_2_1_2_1_1_12"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div><div><i><font color="Green">E17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2_1_1_12_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_2_1_1_12_3"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2
 ;<br/><a NAME="E2:11_2_1_2_1_1_12_3"/><b>then </b>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; not 2 <a href="hidden.html#R2">in</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:11_2_1_2_1_1_12_3"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E9:11_2_1_2_1_1_12"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_2_1_1_12_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_2_1_1_12_4"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 3
 ;<br/><a NAME="E2:11_2_1_2_1_1_12_4"/><b>then </b>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> &amp; not 2 <a href="hidden.html#R2">in</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:11_2_1_2_1_1_12_4"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E9:11_2_1_2_1_1_12"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E14:11_2_1_2_1_1_12"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="yellow11.html#E7:11_2_1_2_1_1_12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="yellow11.html#E10:11_2_1_2_1_1_12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="yellow11.html#E11:11_2_1_2_1_1_12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="yellow11.html#E12:11_2_1_2_1_1_12"><i><font color="Green">E17</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_13"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_13"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_13"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_13"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_13"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_13"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_13"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_13"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_14"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_14"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 )
 ;<br/><div class="add"><a NAME="E2:11_2_1_2_1_1_14"/>
2 <a href="xboole_0.html#R1">misses</a> 3 <a href="subset_1.html#K6">\</a> 2
 <b>by </b><i><a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/><a NAME="E3:11_2_1_2_1_1_14"/><b>then </b>
2 <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E4:11_2_1_2_1_1_14"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2_1_1_14"><i><font color="Green">E12</font></i></a>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E6:11_2_1_2_1_1_14"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E7:11_2_1_2_1_1_14"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E8:11_2_1_2_1_1_14"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E9:11_2_1_2_1_1_14"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E10:11_2_1_2_1_1_14"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E11:11_2_1_2_1_1_14"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_15"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_15"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 )
 ;<br/><div class="add"><a NAME="E2:11_2_1_2_1_1_15"/>
2 <a href="tarski.html#R1">c=</a> 3
 <b>by </b><i><a class="ref" href="card_1.html#T56">CARD_1:56</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2_1_1_15"><i><font color="Green">E12</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E4:11_2_1_2_1_1_15"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E5:11_2_1_2_1_1_15"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E6:11_2_1_2_1_1_15"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E7:11_2_1_2_1_1_15"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E8:11_2_1_2_1_1_15"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E9:11_2_1_2_1_1_15"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_16"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_16"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_16"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_16"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_16"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_16"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_16"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_16"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_17"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_17"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="ref" href="zfmisc_1.html#T19">ZFMISC_1:19</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_17"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_17"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_17"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_17"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_17"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_17"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_18"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_18"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 )
 ;<br/><div class="add"><a NAME="E2:11_2_1_2_1_1_18"/>
2 <a href="xboole_0.html#R1">misses</a> 3 <a href="subset_1.html#K6">\</a> 2
 <b>by </b><i><a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/><a NAME="E3:11_2_1_2_1_1_18"/><b>then </b>
2 <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/><a NAME="E4:11_2_1_2_1_1_18"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2_1_1_18"><i><font color="Green">E12</font></i></a>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E6:11_2_1_2_1_1_18"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E7:11_2_1_2_1_1_18"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E8:11_2_1_2_1_1_18"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E9:11_2_1_2_1_1_18"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E10:11_2_1_2_1_1_18"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E11:11_2_1_2_1_1_18"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_19"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_19"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_19"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_19"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_19"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_19"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_19"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_19"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_20"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_20"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 )
 ;<br/><div class="add"><span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span> <a href="subset_1.html#K8">/\</a> 3 = 
<span class="p1">(<span class="default">3 <a href="xboole_0.html#K3">/\</a> 3</span>)</span> <a href="subset_1.html#K6">\</a> 2
<b>by </b><i><a class="ref" href="xboole_1.html#T49">XBOOLE_1:49</a></i>
<br/>.= 
3 <a href="subset_1.html#K6">\</a> 2

;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2_1_1_20"><i><font color="Green">E12</font></i></a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E4:11_2_1_2_1_1_20"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E5:11_2_1_2_1_1_20"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E6:11_2_1_2_1_1_20"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E7:11_2_1_2_1_1_20"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E8:11_2_1_2_1_1_20"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E9:11_2_1_2_1_1_20"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_21"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_21"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_21"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_21"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_21"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_21"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_21"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_21"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_22"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_22"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 1 )
 ;<br/><div class="add"><span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span> <a href="subset_1.html#K8">/\</a> 3 = 
<span class="p1">(<span class="default">3 <a href="xboole_0.html#K3">/\</a> 3</span>)</span> <a href="subset_1.html#K6">\</a> 1
<b>by </b><i><a class="ref" href="xboole_1.html#T49">XBOOLE_1:49</a></i>
<br/>.= 
3 <a href="subset_1.html#K6">\</a> 1

;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2_1_1_22"><i><font color="Green">E12</font></i></a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E4:11_2_1_2_1_1_22"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E5:11_2_1_2_1_1_22"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E6:11_2_1_2_1_1_22"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E7:11_2_1_2_1_1_22"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E8:11_2_1_2_1_1_22"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E9:11_2_1_2_1_1_22"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_23"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_23"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 2 )
 ;<br/><div class="add"><a NAME="E2:11_2_1_2_1_1_23"/>
2 <a href="tarski.html#R1">c=</a> 3
 <b>by </b><i><a class="ref" href="card_1.html#T56">CARD_1:56</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2_1_1_23"><i><font color="Green">E12</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E4:11_2_1_2_1_1_23"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E5:11_2_1_2_1_1_23"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E6:11_2_1_2_1_1_23"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E7:11_2_1_2_1_1_23"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E8:11_2_1_2_1_1_23"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E9:11_2_1_2_1_1_23"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_24"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_24"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 )
 ;<br/><div class="add"><span class="p1">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span> <a href="subset_1.html#K8">/\</a> 3 = 
<span class="p1">(<span class="default">3 <a href="xboole_0.html#K3">/\</a> 3</span>)</span> <a href="subset_1.html#K6">\</a> 2
<b>by </b><i><a class="ref" href="xboole_1.html#T49">XBOOLE_1:49</a></i>
<br/>.= 
3 <a href="subset_1.html#K6">\</a> 2

;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1_2_1_1_24"><i><font color="Green">E12</font></i></a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E4:11_2_1_2_1_1_24"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E5:11_2_1_2_1_1_24"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E6:11_2_1_2_1_1_24"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E7:11_2_1_2_1_1_24"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E8:11_2_1_2_1_1_24"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E9:11_2_1_2_1_1_24"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_2_1_2_1_1_25"><b>suppose </b></a><a NAME="E1:11_2_1_2_1_1_25"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 3 &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span> ;<br/><b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/><a NAME="E3:11_2_1_2_1_1_25"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><b>hence </b><a NAME="E4:11_2_1_2_1_1_25"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="enumset1.html#K3">{</a><span class="default">0,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 1</span>)</span>,2,<span class="p3">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span></span>)</span>;<br/><b>assume </b><a NAME="E5:11_2_1_2_1_1_25"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><a NAME="E6:11_2_1_2_1_1_25"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E7:11_2_1_2_1_1_25"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/><b>hence </b><a NAME="E8:11_2_1_2_1_1_25"/>
<font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:11_2_1"/>
(  <a href="yellow11.html#K1" target="_self">N_5</a>  is <a href="lattice3.html#V2">with_infima</a> &amp;  <a href="yellow11.html#K1" target="_self">N_5</a>  is <a href="lattice3.html#V1">with_suprema</a> )
 <b>by </b><i><a class="txt" href="yellow11.html#E1:11_2_1"><i><font color="Green">E10</font></i></a></i>;<br/>


</div>
