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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a>  <a href="orders_2.html#L1">RelStr</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> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_1.html#D3">RELAT_1:def 3</a><br/>



<a NAME="E1:33"/><i><font color="Green">E21</font></i>: 
 <a href="waybel28.html#K3" target="_self">lim_inf-Convergence</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_6.html#K7">NetUniv</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D21">YELLOW_6:def 21</a></i>;<br/>
<b>assume </b><a NAME="E2:33"/><i><font color="Green">E22</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="waybel28.html#K3" target="_self">lim_inf-Convergence</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:33"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7">NetUniv</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="waybel28.html#E1:33"><i><font color="Green">E21</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being  <a href="waybel_0.html#V6">strict</a> <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:33"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E6:33"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K2">the_universe_of</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="yellow_6.html#D14">YELLOW_6:def 14</a></i>;<br/>
<a NAME="E7:33"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K7">NetUniv</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="waybel28.html#E1:33"><i><font color="Green">E21</font></i></a>, <a class="txt" href="waybel28.html#E2:33"><i><font color="Green">E22</font></i></a>, <a class="txt" href="waybel28.html#E5:33"><i><font color="Green">E23</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="waybel28.html#E1:33"><i><font color="Green">E21</font></i></a>, <a class="txt" href="waybel28.html#E2:33"><i><font color="Green">E22</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E9:33"/>
<font color="Maroon">c<sub>4</sub></font> is    <a href="yellow_6.html#M2">subnet</a> of <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_6.html#T23">YELLOW_6:23</a></i>;<br/>
<a NAME="E10:33"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K1">lim_inf</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="waybel28.html#E2:33"><i><font color="Green">E22</font></i></a>, <a class="txt" href="waybel28.html#E5:33"><i><font color="Green">E23</font></i></a>, <a class="txt" href="waybel28.html#E7:33"><i><font color="Green">E24</font></i></a>, <a class="ref" href="waybel28.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E11:33"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="waybel11.html#R1">is_S-limit_of</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="waybel11.html#D7">WAYBEL11:def 7</a></i>;<br/>
<b>hence </b><a NAME="E12:33"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K2">Scott-Convergence</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="waybel28.html#E5:33"><i><font color="Green">E23</font></i></a>, <a class="txt" href="waybel28.html#E7:33"><i><font color="Green">E24</font></i></a>, <a class="ref" href="waybel11.html#D8">WAYBEL11:def 8</a></i>;<br/>


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