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<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:61_1_1"/><i><font color="Green">E38</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</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">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<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">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D35">WAYBEL_0:def 35</a><br/>

<b>assume </b><a NAME="E2:61_1_1"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span>, <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D31">WAYBEL_0:def 31</a><br/>

<a NAME="E3:61_1_1"/>
<span class="p1">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="domain_1.html#K7">}</a></span>
 
<b>by </b><i><a class="txt" href="waybel_2.html#E1:61_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T118">FUNCT_1:118</a></i>;<br/>
<b>hence </b><a NAME="E4:61_1_1"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T20">YELLOW_0:20</a></i>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="waybel_0.html#NM3">Ideal</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="yellow_2.html#T43">YELLOW_2:43</a></i>;<br/>
<a NAME="E6:61_1_1"/><i><font color="Green">E39</font></i>: 
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>5</sub></font> <a href="yellow_4.html#K2">"\/"</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="waybel_0.html#T75">WAYBEL_0:75</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">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span></span>)</span> = 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="domain_1.html#K7">}</a></span>
<b>by </b><i><a class="txt" href="waybel_2.html#E1:61_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="funct_1.html#T118">FUNCT_1:118</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_2.html#D3">YELLOW_2:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_2.html#D3">YELLOW_2:def 3</a></i>
<br/>.= 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="yellow_4.html#K2">"\/"</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="waybel_2.html#T4" target="_self">Th4</a></i>
<br/>.= 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="yellow_4.html#K2">"\/"</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="waybel_2.html#E6:61_1_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="waybel_0.html#T33">WAYBEL_0:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K3">downarrow</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="yellow_4.html#K2">"\/"</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow_2.html#D3">YELLOW_2:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_4.html#T30">YELLOW_4:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow_2.html#K2">SupMap</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K7">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>
;<br/>


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