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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="waybel_1.html#V2">distributive</a> <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>assume </b><a NAME="E1:35"/>
<font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  is <a href="waybel_2.html#V2">meet-continuous</a>
 ;<br/>

<a NAME="E2:35"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a>  is <a href="waybel_2.html#V1">satisfying_MC</a>
 
<b>by </b><i><a class="ref" href="waybel_2.html#D7">WAYBEL_2:def 7</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E3:35"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel16.html#V1" target="_self">completely-irreducible</a>
 ;<br/>

<a NAME="E4:35"/>
not  <a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel16.html#K1" target="_self">Irr</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="waybel16.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E5:35"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="waybel16.html#E3:35"><i><font color="Green">E23</font></i></a>, <a class="ref" href="waybel16.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E6:35"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_6.html#V2">meet-irreducible</a>
 
<b>by </b><i><a class="txt" href="waybel16.html#E3:35"><i><font color="Green">E23</font></i></a>, <a class="ref" href="waybel16.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E7:35"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_6.html#V5">prime</a>
 
<b>by </b><i><a class="ref" href="waybel_6.html#T27">WAYBEL_6:27</a></i>;<br/>
<a NAME="E8:35"/><b>then </b>
<span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K3">`</a>  is   <a href="waybel_0.html#NM4">Filter</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="waybel16.html#E5:35"><i><font color="Green">E24</font></i></a>, <a class="ref" href="waybel_6.html#T26">WAYBEL_6:26</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> as   <a href="waybel_0.html#NM4">Filter</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="subset_1.html#D5">SUBSET_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E11:35"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R2">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E12:35"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R2">&lt;</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E13:35"/>
 <a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6">uparrow</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel16.html#E3:35"><i><font color="Green">E23</font></i></a>, <a class="ref" href="waybel16.html#T20" target="_self">Th20</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>] means ( <font color="Maroon">a<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> &amp; not <font color="Maroon">a<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> );<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>from </b><i><a class="ref" href="domain_1.html#S7">DOMAIN_1:sch 7</a>();<br/></i>
<a NAME="E15:35"/>
not <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="waybel16.html#E11:35"><i><font color="Green">E25</font></i></a>, <a class="ref" href="orders_2.html#T30">ORDERS_2:30</a></i>;<br/>
<a NAME="E16:35"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:35_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E2:35_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><b>take </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>7</sub></font>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:35_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E5:35_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E6:35_1"/><i><font color="Green">E32</font></i>: 
not <font color="Maroon">c<sub>9</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E1:35_1"><i><font color="Green">E28</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:35_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E9:35_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E10:35_1"/><i><font color="Green">E35</font></i>: 
not <font color="Maroon">c<sub>10</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E2:35_1"><i><font color="Green">E29</font></i></a></i>;<br/><a NAME="E11:35_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E12:35_1"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E4:35_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="waybel16.html#E5:35_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/><a NAME="E13:35_1"/>
not <font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:35_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:35_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="waybel16.html#E11:35"><i><font color="Green">E25</font></i></a>, <a class="ref" href="orders_2.html#D10">ORDERS_2:def 10</a></i>;<br/>
<div><i><font color="Green">E40</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:35_1_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>and </b><br/><a NAME="E2:35_1_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E3:35_1_1_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="orders_2.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E8:35_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="waybel16.html#E10:35_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="waybel16.html#E1:35_1_1_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="waybel16.html#E2:35_1_1_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="orders_2.html#D10">ORDERS_2:def 10</a></i>;<br/><b>hence </b><a NAME="E4:35_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E12:35"><i><font color="Green">E26</font></i></a></i>;<br/></div><b>end;</b></div>
<font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="waybel16.html#E4:35_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="waybel16.html#E5:35_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel16.html#E8:35_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="waybel16.html#E9:35_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="waybel16.html#E2:35_1_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="waybel16.html#E3:35_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="waybel_1.html#D3">WAYBEL_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="waybel_1.html#T6">WAYBEL_1:6</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel16.html#E11:35_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="waybel16.html#E1:35_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>
;<br/>
<b>hence </b><a NAME="E5:35_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="waybel16.html#E4:35_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="waybel16.html#E6:35_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E14:35_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E12:35_1"><i><font color="Green">E37</font></i></a></i>;<br/><b>thus </b><a NAME="E15:35_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><b>thus </b><a NAME="E16:35_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V2">filtered</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="waybel16.html#E16:35"><i><font color="Green">E27</font></i></a>, <a class="ref" href="waybel_0.html#D2">WAYBEL_0:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="yellow_7.html#NK1" target="_self">opp</a> </span>)</span> <b>by </b><i><a class="ref" href="yellow_7.html#T27">YELLOW_7:27</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:35_2"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><b>take </b><font color="Maroon">c<sub>9</sub></font> =  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>6</sub></font>;<br/><b>thus </b><a NAME="E2:35_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:35_2_1"/>
 <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T17">YELLOW_0:17</a></i>;<br/>
<a NAME="E2:35_2_1"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_7.html#T13">YELLOW_7:13</a></i>;<br/>
<a NAME="E3:35_2_1"/><i><font color="Green">E30</font></i>: 
 <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8">~</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T17">YELLOW_0:17</a></i>;<br/>
<a NAME="E4:35_2_1"/><i><font color="Green">E31</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8">~</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="lattice3.html#D6">LATTICE3:def 6</a></i>;<br/>
<b>assume </b><a NAME="E5:35_2_1"/>
not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E6:35_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E7:35_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T17">WAYBEL_0:17</a></i>;<br/>
<b>then </b><i><font color="Green">E32</font></i>: <font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8">~</a> </span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="lattice3.html#K8">~</a> </span>)</span>
<b>by </b><i><a class="ref" href="yellow_7.html#T23">YELLOW_7:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8">~</a> </span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel16.html#E2:35_2_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="lattice3.html#D6">LATTICE3:def 6</a></i>
<br/>.= 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8">~</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel16.html#E2:35"><i><font color="Green">E22</font></i></a>, <a class="ref" href="waybel_2.html#D6">WAYBEL_2:def 6</a></i>
<br/>.= 
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K8">~</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="waybel16.html#E3:35_2_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="yellow_7.html#T13">YELLOW_7:13</a></i>
<br/>.= 
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K2">"\/"</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="waybel16.html#E4:35_2_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="waybel16.html#T5" target="_self">Th5</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:35_2_1_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K2">"\/"</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:35_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> </span>}</span> 
 <b>by </b><i><a class="ref" href="yellow_4.html#T15">YELLOW_4:15</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:35_2_1_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>11</sub></font>
 <b>and </b><br/><a NAME="E5:35_2_1_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E6:35_2_1_2"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E4:35_2_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:35_2_1_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>and </b><br/><a NAME="E9:35_2_1_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E10:35_2_1_2"/><i><font color="Green">E37</font></i>: 
not <font color="Maroon">c<sub>12</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E5:35_2_1_2"><i><font color="Green">E34</font></i></a></i>;<br/><a NAME="E11:35_2_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E4:35_2_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="waybel16.html#E8:35_2_1_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="waybel16.html#E10:35_2_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>;<br/><a NAME="E12:35_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R2">&lt;</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E6:35_2_1_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="orders_2.html#D10">ORDERS_2:def 10</a></i>;<br/><b>hence </b><a NAME="E13:35_2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E12:35"><i><font color="Green">E26</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E10:35_2_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="lattice3.html#R1">is_&lt;=_than</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K2">"\/"</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/>
<a NAME="E11:35_2_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="waybel16.html#E8:35_2_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="yellow_0.html#T33">YELLOW_0:33</a></i>;<br/>
<b>hence </b><a NAME="E12:35_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="waybel16.html#E11:35"><i><font color="Green">E25</font></i></a>, <a class="ref" href="orders_2.html#T30">ORDERS_2:30</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:35_2"/><b>then </b>
not <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:35_2"/><b>then </b><i><font color="Green">E29</font></i>: 
not <font color="Maroon">c<sub>9</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="waybel_0.html#T17">WAYBEL_0:17</a></i>;<br/><a NAME="E5:35_2"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E6:35_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T33">YELLOW_0:33</a></i>;<br/><a NAME="E7:35_2"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</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_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E8:35_2"/>
not <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E1:35_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E9:35_2"/><b>then </b>
not <font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="waybel_0.html#T17">WAYBEL_0:17</a></i>;<br/><a NAME="E10:35_2"/><b>then </b>
not <font color="Maroon">c<sub>8</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E11:35"><i><font color="Green">E25</font></i></a>, <a class="txt" href="waybel16.html#E12:35"><i><font color="Green">E26</font></i></a>, <a class="ref" href="waybel16.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E11:35_2"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E7:35_2"><i><font color="Green">E32</font></i></a></i>;<br/><a NAME="E12:35_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E6:35_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/><a NAME="E13:35_2"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E5:35_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>10</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:35_2_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>10</sub></font>
 ;<br/><a NAME="E2:35_2_2"/>
not <font color="Maroon">c<sub>10</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:35_2_2_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<a NAME="E2:35_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T37">XBOOLE_1:37</a></i>;<br/>
<a NAME="E3:35_2_2_1"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>10</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_7.html#T3">WAYBEL_7:3</a></i>;<br/>
<a NAME="E4:35_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel16.html#E1:35_2_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/>
<b>hence </b><a NAME="E5:35_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="waybel16.html#E4:35_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="waybel_0.html#T34">WAYBEL_0:34</a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon">c<sub>11</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:35_2_2"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>11</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="waybel16.html#E4:35_2_2"><i><font color="Green">E35</font></i></a></i>;<br/><b>take </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>12</sub></font>;<br/><b>thus </b><a NAME="E6:35_2_2"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E4:35_2_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E7:35_2_2"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</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_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E8:35_2_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T33">YELLOW_0:33</a></i>;<br/><a NAME="E9:35_2_2"/>
not <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E4:35_2_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E10:35_2_2"/><b>then </b>
not <font color="Maroon">c<sub>13</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="waybel_0.html#T17">WAYBEL_0:17</a></i>;<br/><a NAME="E11:35_2_2"/><b>then </b>
not <font color="Maroon">c<sub>13</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E11:35"><i><font color="Green">E25</font></i></a>, <a class="txt" href="waybel16.html#E12:35"><i><font color="Green">E26</font></i></a>, <a class="ref" href="waybel16.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E12:35_2_2"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E7:35_2_2"><i><font color="Green">E36</font></i></a></i>;<br/><a NAME="E13:35_2_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E8:35_2_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a></i>;<br/><b>hence </b><a NAME="E14:35_2_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E7:35_2_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/></div><b>end;</b></div><a NAME="E15:35_2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="waybel_3.html#D1">WAYBEL_3:def 1</a></i>;<br/><b>hence </b><a NAME="E16:35_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="waybel16.html#E13:35_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="waybel_3.html#T2">WAYBEL_3:2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E21:35"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is  <a href="waybel_6.html#V1">Open</a> <a href="waybel_0.html#NM4">Filter</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="waybel_6.html#D1">WAYBEL_6:def 1</a></i>;<br/>


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