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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattice3.html#V3">complete</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:69"/><i><font color="Green">E20</font></i>: 
 <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</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="E2:69"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#NR3" target="_self">is_&gt;=_than</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#NR3" target="_self">is_&gt;=_than</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T33">YELLOW_0:33</a></i>;<br/>
<a NAME="E3:69"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#NR3" target="_self">is_&gt;=_than</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_4.html#T55" target="_self">Th55</a></i>;<br/>
<a NAME="E4:69"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow_4.html#E1:69"><i><font color="Green">E20</font></i></a>, <a class="ref" href="yellow_0.html#D10">YELLOW_0:def 10</a></i>;<br/>
<a NAME="E5:69"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#NR3" target="_self">is_&gt;=_than</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#NR3" target="_self">is_&gt;=_than</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="yellow_4.html#T54" target="_self">Th54</a></i>;<br/>
<a NAME="E6:69"/><b>then </b>
(  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T33">YELLOW_0:33</a></i>;<br/>
<a NAME="E7:69"/><b>then </b><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E8:69"/>
<span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/>
<b>hence </b><a NAME="E9:69"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow_4.html#E4:69"><i><font color="Green">E21</font></i></a>, <a class="txt" href="yellow_4.html#E7:69"><i><font color="Green">E22</font></i></a>, <a class="ref" href="orders_2.html#T25">ORDERS_2:25</a></i>;<br/>


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