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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="hidden.html#M1">set</a> ;<br/>



<a NAME="E1:1"/>
(  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="yellow_0.html#R2">ex_inf_of</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/>
<b>hence </b><a NAME="E2:1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> implies (  <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="yellow_0.html#K2">"/\"</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a>  <a href="yellow_0.html#K2">"/\"</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#T34">YELLOW_0:34</a>, <a class="ref" href="yellow_0.html#T35">YELLOW_0:35</a></i>;<br/>


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