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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="waybel_0.html#V24">up-complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>2</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>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nattra_1.html#K1">|</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E1:31"/><i><font color="Green">E19</font></i>: 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nattra_1.html#K1">|</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="funct_3.html#T1">FUNCT_3:1</a></i>;<br/>
 <a href="waybel11.html#K1">lim_inf</a> <span class="p1">(<span class="default"><a href="waybel17.html#K4" target="_self">Net-Str</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <a href="waybel_2.html#K1">sup</a> <span class="p1">(<span class="default"><a href="waybel17.html#K4" target="_self">Net-Str</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel17.html#E19"><i><font color="Green">Lemma17</font></i></a></i>
<br/>.= 
 <a href="yellow_2.html#NK6" target="_self">Sup</a> 
<b>by </b><i><a class="ref" href="waybel_2.html#D1">WAYBEL_2:def 1</a></i>
<br/>.= 
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nattra_1.html#K1">|</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="yellow_2.html#D5">YELLOW_2:def 5</a></i>
<br/>.= 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="waybel17.html#E1:31"><i><font color="Green">E19</font></i></a>, <a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>
;<br/>
<b>hence </b><a NAME="E3:31"/>
 <a href="waybel11.html#K1">lim_inf</a> <span class="p1">(<span class="default"><a href="waybel17.html#K4" target="_self">Net-Str</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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