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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="waybel_0.html#NM6">Semilattice</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:76"/><i><font color="Green">E29</font></i>: 
<span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span> is <a href="waybel_0.html#V24">up-complete</a>
 <b>and </b><br/><a NAME="E2:76"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span><br/>for <font color="Olive">b<sub>2</sub></font> being 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"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span> holds <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <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"><font color="Olive">b<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <font color="Olive">b<sub>2</sub></font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_2.html#D6">WAYBEL_2:def 6</a>,<a class="ref" href="waybel_2.html#D7">WAYBEL_2:def 7</a><br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_2.html#D6">WAYBEL_2:def 6</a>,<a class="ref" href="waybel_2.html#D7">WAYBEL_2:def 7</a>
<div class="add"><b>thus </b><a NAME="E1:76_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V24">up-complete</a>
 <b>by </b><i><a class="txt" href="yellow10.html#E1:76"><i><font color="Green">E29</font></i></a>, <a class="ref" href="waybel_2.html#T11">WAYBEL_2:11</a></i>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</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>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K6">}</a></span> 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 <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="waybel_0.html#T5">WAYBEL_0:5</a></i>;<br/><a NAME="E4:76_1"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span>,<span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E1:76"><i><font color="Green">E29</font></i></a>, <a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a></i>;<br/><a NAME="E5:76_1"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p4"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p4"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 <b>by </b><i><a class="ref" href="yellow_3.html#T46">YELLOW_3:46</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> 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"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <b>by </b><i><a class="ref" href="waybel_0.html#T5">WAYBEL_0:5</a></i>;<br/><a NAME="E7:76_1"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>7</sub></font> <a href="yellow_4.html#K4">"/\"</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span>,<span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>
 <b>by </b><i><a class="txt" href="yellow10.html#E1:76"><i><font color="Green">E29</font></i></a>, <a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a></i>;<br/><a NAME="E8:76_1"/><b>then </b><i><font color="Green">E32</font></i>: 
 <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"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <span class="p2"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p4">(<span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><span class="p0"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <span class="p5"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p4">(<span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><span class="p0"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <span class="p5"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 <b>by </b><i><a class="ref" href="yellow_3.html#T46">YELLOW_3:46</a></i>;<br/><b>thus </b> <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"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="yellow_4.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_5.html#T15">FUNCT_5:15</a></i>
<br/>.= 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="yellow_4.html#K4">"/\"</a> <span class="p2">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_5.html#T11">FUNCT_5:11</a></i>
<br/>.= 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow10.html#T24" target="_self">Th24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span> <a href="yellow_3.html#K8">`1</a> 
<b>by </b><i><a class="txt" href="yellow10.html#E8:76_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span> <a href="yellow_3.html#K8">`1</a> 
<b>by </b><i><a class="txt" href="yellow10.html#E2:76"><i><font color="Green">E30</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="yellow_3.html#K8">`1</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#NK3" target="_self">sup</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span> <a href="yellow_3.html#K8">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="yellow10.html#T13" target="_self">Th13</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span> <a href="yellow_3.html#K8">`1</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p2">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="yellow10.html#E5:76_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <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>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_5.html#T11">FUNCT_5:11</a></i>
;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E4:76"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V24">up-complete</a>
 <b>by </b><i><a class="txt" href="yellow10.html#E1:76"><i><font color="Green">E29</font></i></a>, <a class="ref" href="waybel_2.html#T11">WAYBEL_2:11</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_2.html#D7">WAYBEL_2:def 7</a><br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_2.html#D6">WAYBEL_2:def 6</a><br/><b>let </b><font color="Maroon">c<sub>4</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>2</sub></font>;<br/>



<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K6">}</a></span> 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 <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="waybel_0.html#T5">WAYBEL_0:5</a></i>;<br/>
<a NAME="E7:76"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span>,<span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>
 
<b>by </b><i><a class="txt" href="yellow10.html#E1:76"><i><font color="Green">E29</font></i></a>, <a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a></i>;<br/>
<a NAME="E8:76"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p4"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p4"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T46">YELLOW_3:46</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> 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"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <b>by </b><i><a class="ref" href="waybel_0.html#T5">WAYBEL_0:5</a></i>;<br/>
<a NAME="E10:76"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>7</sub></font> <a href="yellow_4.html#K4">"/\"</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span>,<span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>
 
<b>by </b><i><a class="txt" href="yellow10.html#E1:76"><i><font color="Green">E29</font></i></a>, <a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a></i>;<br/>
<a NAME="E11:76"/><b>then </b><i><font color="Green">E32</font></i>: 
 <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"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <span class="p2"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p4">(<span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><span class="p0"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <span class="p5"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p4">(<span class="default"><span class="p5"><a href="domain_1.html#K6">{</a><span class="default"><span class="p0"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <span class="p5"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T46">YELLOW_3:46</a></i>;<br/>
<b>thus </b> <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"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="yellow_4.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_5.html#T15">FUNCT_5:15</a></i>
<br/>.= 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="yellow_4.html#K4">"/\"</a> <span class="p2">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_5.html#T11">FUNCT_5:11</a></i>
<br/>.= 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow10.html#T24" target="_self">Th24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p2">(<span class="default"><span class="p3"><a href="domain_1.html#K6">{</a><span class="default"><span class="p4"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="yellow_3.html#K7">]</a></span></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K4">"/\"</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span> <a href="yellow_3.html#K9">`2</a> 
<b>by </b><i><a class="txt" href="yellow10.html#E11:76"><i><font color="Green">E32</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span> <a href="yellow_3.html#K9">`2</a> 
<b>by </b><i><a class="txt" href="yellow10.html#E2:76"><i><font color="Green">E30</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="yellow_3.html#K7">]</a></span> <a href="yellow_3.html#K9">`2</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#NK3" target="_self">sup</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span> <a href="yellow_3.html#K9">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="yellow10.html#T13" target="_self">Th13</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span> <a href="yellow_3.html#K9">`2</a> </span>)</span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p2">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p3"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="yellow10.html#E8:76"><i><font color="Green">E31</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <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>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_5.html#T11">FUNCT_5:11</a></i>
;<br/>


</div>
