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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="waybel_3.html#V3">continuous</a> <a href="lattice3.html#V3">complete</a> <a href="waybel19.html#V2">Lawson</a> <a href="waybel_9.html#NM1">TopLattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>given </b><font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:60"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:60"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="pre_topc.html#V4">closed</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D4">WAYBEL_0:def 4</a><br/>

<b>assume </b><a NAME="E3:60"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as  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> <b>by </b><i><a class="ref" href="yellow_2.html#T7">YELLOW_2:7</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>assume </b><a NAME="E5:60"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E6:60"/>
( the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">c<sub>4</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="waybel21.html#T32" target="_self">Th32</a></i>;<br/>
<a NAME="E7:60"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<a NAME="E8:60"/><b>then </b>
 <a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">c<sub>5</sub></font> <a href="waybel_0.html#R1">is_eventually_in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="waybel21.html#E1:60"><i><font color="Green">E38</font></i></a>, <a class="ref" href="waybel21.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E9:60"/><b>then </b>
 <a href="yellow_6.html#K11">Lim</a> <span class="p1">(<span class="default"><a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="waybel19.html#T26">WAYBEL19:26</a></i>;<br/>
<a NAME="E10:60"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="yellow_6.html#K11">Lim</a> <span class="p1">(<span class="default"><a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="waybel21.html#E2:60"><i><font color="Green">E39</font></i></a>, <a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>;<br/>
<a NAME="E11:60"/>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K11">Lim</a> <span class="p1">(<span class="default"><a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel21.html#T35" target="_self">Th35</a></i>;<br/>
<b>hence </b><a NAME="E12:60"/>
 <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel21.html#E1:60"><i><font color="Green">E38</font></i></a>, <a class="txt" href="waybel21.html#E10:60"><i><font color="Green">E40</font></i></a></i>;<br/>


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