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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:16"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><br/> for <font color="Olive">N</font> being  <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">L</font>  st <font color="Olive">N</font> is <a href="waybel_0.html#V10">eventually-directed</a> holds <br/><font color="Olive">x</font> <a href="lattice3.html#K11">"/\"</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K1">sup</a> <font color="Olive">N</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K3">"/\"</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <font color="Olive">N</font>,<font color="Maroon">L</font></span>)</span></span>)</span></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_2.html#D6">WAYBEL_2:def 6</a><br/><b>let </b><font color="Maroon">D</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">L</font>;<br/>



<b>reconsider </b><font color="Maroon">n</font> =  <a href="partfun1.html#K6">id</a> <font color="Maroon">D</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">D</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <b>by </b><i><a class="ref" href="funct_2.html#T9">FUNCT_2:9</a></i>;<br/>
<b>set </b><font color="Maroon">N</font> =  <a href="waybel_0.html#G1">NetStr</a>(# <font color="Maroon">D</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">D</font></span>)</span>,<font color="Maroon">n</font> #);<br/>
<a NAME="E3:16"/>
<font color="Maroon">D</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 
;<br/>
<b>then </b><i><font color="Green">E34</font></i>: <font color="Maroon">D</font> = 
<font color="Maroon">n</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">D</font>
<b>by </b><i><a class="ref" href="funct_1.html#T162">FUNCT_1:162</a></i>
<br/>.= 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K1">netmap</a> <a href="waybel_0.html#G1">NetStr</a>(# <font color="Maroon">D</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">D</font></span>)</span>,<font color="Maroon">n</font> #),<font color="Maroon">L</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T45">FUNCT_2:45</a></i>
;<br/>
<a NAME="E5:16"/><i><font color="Green">E35</font></i>: 
 <a href="waybel_0.html#G1">NetStr</a>(# <font color="Maroon">D</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">D</font></span>)</span>,<font color="Maroon">n</font> #) is <a href="waybel_0.html#V10">eventually-directed</a>
 
<b>by </b><i><a class="ref" href="waybel_2.html#T20">WAYBEL_2:20</a></i>;<br/>
<a NAME="E6:16"/><i><font color="Green">E36</font></i>: 
 <a href="yellow_2.html#NK6" target="_self">Sup</a>  <a href="hidden.html#R1">=</a>  <a href="waybel_2.html#K1">sup</a> <a href="waybel_0.html#G1">NetStr</a>(# <font color="Maroon">D</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">D</font></span>)</span>,<font color="Maroon">n</font> #)
 
;<br/>
<b>thus </b><font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font></span>)</span> = 
<font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <span class="p1">(<span class="default"><a href="yellow_2.html#NK6" target="_self">Sup</a> </span>)</span>
<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> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K3">"/\"</a> <font color="Maroon">D</font></span>)</span>
<b>by </b><i>, , , </i>
;<br/>


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