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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_0.html#NM7">sup-Semilattice</a>;<br/>

<b>assume </b><a NAME="E1:39_2_1"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V24">up-complete</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_3.html#V2" target="_self">satisfying_axiom_of_approximation</a> )
 ;<br/>

<b>thus </b><a NAME="E2:39_2_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( not  <a href="waybel_3.html#K1" target="_self">waybelow</a> <font color="Olive">b<sub>1</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp;  <a href="waybel_3.html#K1" target="_self">waybelow</a> <font color="Olive">b<sub>1</sub></font> is <a href="waybel_0.html#V1">directed</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_3.html#D6" target="_self">WAYBEL_3:def 6</a><br/>

<b>thus </b><a NAME="E3:39_2_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V24">up-complete</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_3.html#V2" target="_self">satisfying_axiom_of_approximation</a> )
 <b>by </b><i><a class="txt" href="waybel_3.html#E1:39_2_1"><i><font color="Green">E18</font></i></a></i>;<br/>


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