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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <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>assume </b><a NAME="E1:31"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">b<sub>1</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font> being <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">b<sub>2</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>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D1" target="_self">WAYBEL_3:def 1</a><br/>

<b>assume </b><a NAME="E2:31"/>
<font color="Maroon">c<sub>3</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>4</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:31"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</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>5</sub></font> )
 <b>by </b><i><a class="txt" href="waybel_3.html#E1:31"><i><font color="Green">E15</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="waybel_3.html#E4:31"><i><font color="Green">E16</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</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="E7:31"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="ref" href="waybel_0.html#T1">WAYBEL_0:1</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<a NAME="E8:31"/>
<font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="waybel_3.html#E7:31"><i><font color="Green">E17</font></i></a>, <a class="ref" href="yellow_0.html#T32">YELLOW_0:32</a></i>;<br/>
<b>hence </b><a NAME="E9:31"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="waybel_3.html#E4:31"><i><font color="Green">E16</font></i></a>, <a class="txt" href="waybel_3.html#E7:31"><i><font color="Green">E17</font></i></a>, <a class="ref" href="yellow_0.html#D2">YELLOW_0:def 2</a></i>;<br/>


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