<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon" title="c2">S</font> =  <a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">R</font>;<br/>
<b>let </b><font color="Maroon" title="c3">N</font> be   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">R</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D24" title="YELLOW_6:def.24">YELLOW_6:def 24</a><br/><b>let </b><font color="Maroon" title="c4">Y</font> be    <a href="yellow_6.html#M2" title="YELLOW_6:mode.2">subnet</a> of <font color="Maroon" title="c3">N</font>;<br/>



<a NAME="E1:70_1_1"/><i><font color="Green" title="E40">A1</font></i>: 
 <a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c1">R</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D21" title="YELLOW_6:def.21">YELLOW_6:def 21</a></i>;<br/>
<b>assume </b><a NAME="E2:70_1_1"/><i><font color="Green" title="E41">A2</font></i>: 
<font color="Maroon" title="c4">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c1">R</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">Y'</font> being  <a href="waybel_0.html#V6" title="WAYBEL_0:attr.6">strict</a> <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E4:70_1_1"/><i><font color="Green" title="E42">A3</font></i>: 
<font color="Maroon" title="c5">Y'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y</font>
 <b>and </b><br/><a NAME="E5:70_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">Y'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K2" title="YELLOW_6:func.2">the_universe_of</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="ref" href="yellow_6.html#D14" title="YELLOW_6:def.14">YELLOW_6:def 14</a></i>;<br/>
<b>let </b><font color="Maroon" title="c6">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c7">p'</font> = <font color="Maroon" title="c6">p</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> ;<br/>
<b>assume </b><a NAME="E7:70_1_1"/><i><font color="Green" title="E43">A4</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">N</font>,<font color="Maroon" title="c6">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">R</font>
 ;<br/>

<a NAME="E8:70_1_1"/><b>then </b><i><font color="Green" title="E44">A5</font></i>: 
<font color="Maroon" title="c3">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E1:70_1_1"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">N'</font> being  <a href="waybel_0.html#V6" title="WAYBEL_0:attr.6">strict</a> <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E10:70_1_1"/><i><font color="Green" title="E45">A6</font></i>: 
<font color="Maroon" title="c8">N'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">N</font>
 <b>and </b><br/><a NAME="E11:70_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c8">N'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K2" title="YELLOW_6:func.2">the_universe_of</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="ref" href="yellow_6.html#D14" title="YELLOW_6:def.14">YELLOW_6:def 14</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font>) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font> =  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c3">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c1">R</font> </span>}</span> ,<font color="Maroon" title="c1">R</font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>verum;<br/>
<b>reconsider </b><font color="Maroon" title="c9">X1</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">j</font>) where <font color="Olive" title="b1">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">j</font>] </span>}</span>  as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font> <b>from </b><i><a class="ref" href="domain_1.html#S8" title="DOMAIN_1:sch.8">DOMAIN_1:sch 8</a>();<br/></i>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font>) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font> =  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Y</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c1">R</font> </span>}</span> ,<font color="Maroon" title="c1">R</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">X2</font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">j</font>) where <font color="Olive" title="b1">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">j</font>] </span>}</span>  as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font> <b>from </b><i><a class="ref" href="domain_1.html#S8" title="DOMAIN_1:sch.8">DOMAIN_1:sch 8</a>();<br/></i>
<a NAME="E14:70_1_1"/>
<font color="Maroon" title="c6">p</font> <a href="waybel11.html#R1" title="WAYBEL11:pred.1">is_S-limit_of</a> <font color="Maroon" title="c8">N'</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E7:70_1_1"><i><font color="Green" title="E43">A4</font></i></a>, <a class="txt" href="waybel11.html#E8:70_1_1"><i><font color="Green" title="E44">A5</font></i></a>, <a class="txt" href="waybel11.html#E10:70_1_1"><i><font color="Green" title="E45">A6</font></i></a>, <a class="ref" href="waybel11.html#D8" target="_self" title="WAYBEL11:def.8">Def8</a></i>;<br/>
<a NAME="E15:70_1_1"/><b>then </b><i><font color="Green" title="E46">A7</font></i>: 
<font color="Maroon" title="c6">p</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <font color="Maroon" title="c3">N</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E10:70_1_1"><i><font color="Green" title="E45">A6</font></i></a>, <a class="ref" href="waybel11.html#D7" target="_self" title="WAYBEL11:def.7">Def7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c11">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c4">Y</font>,<font color="Maroon" title="c3">N</font><b> such that </b><br/><a NAME="E17:70_1_1"/><i><font color="Green" title="E47">A8</font></i>: 
the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c4">Y</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c3">N</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c11">f</font>
 <b>and </b><br/><a NAME="E18:70_1_1"/><i><font color="Green" title="E48">A9</font></i>: 
for <font color="Olive" title="b1">m</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font>  ex <font color="Olive" title="b2">n</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font> st <br/>for <font color="Olive" title="b3">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font>  st <font color="Olive" title="b2">n</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b3">p</font> holds <br/><font color="Olive" title="b1">m</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c11">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Olive" title="b3">p</font>
 <b>by </b><i><a class="ref" href="yellow_6.html#D12" title="YELLOW_6:def.12">YELLOW_6:def 12</a></i>;<br/>
<a NAME="E19:70_1_1"/>
<font color="Maroon" title="c9">X1</font> <a href="yellow_4.html#R3" title="YELLOW_4:pred.3">is_finer_than</a> <font color="Maroon" title="c10">X2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c12">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_4.html#D1" title="YELLOW_4:def.1">YELLOW_4:def 1</a><br/>

<b>assume </b><a NAME="E1:70_1_1_1"/>
<font color="Maroon" title="c12">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">X1</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c13">j</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font><b> such that </b><br/><a NAME="E3:70_1_1_1"/><i><font color="Green" title="E49">A10</font></i>: 
<font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c3">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c13">j</font> </span>}</span> ,<font color="Maroon" title="c1">R</font>
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c14">j</font> = <font color="Maroon" title="c13">j</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font> ;<br/>
<b>consider </b><font color="Maroon" title="c15">n</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font><b> such that </b><br/><a NAME="E6:70_1_1_1"/><i><font color="Green" title="E50">A11</font></i>: 
for <font color="Olive" title="b1">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font>  st <font color="Maroon" title="c15">n</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b1">p</font> holds <br/><font color="Maroon" title="c14">j</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c11">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Olive" title="b1">p</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E18:70_1_1"><i><font color="Green" title="E48">A9</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c16">X3</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Y</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c15">n</font> </span>}</span> ;<br/>
<b>set </b><font color="Maroon" title="c17">X4</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c3">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c14">j</font> </span>}</span> ;<br/>
<b>take </b><font color="Maroon" title="c18">b</font> =  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Y</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c15">n</font> </span>}</span> ,<font color="Maroon" title="c1">R</font>;<br/>

<b>thus </b><a NAME="E7:70_1_1_1"/>
<font color="Maroon" title="c18">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">X2</font>
 ;<br/>

<a NAME="E8:70_1_1_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Y</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c15">n</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c3">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c14">j</font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c19">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:70_1_1_1_1"/>
<font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c4">Y</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c15">n</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c20">m</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font><b> such that </b><br/><a NAME="E3:70_1_1_1_1"/><i><font color="Green" title="E51">A12</font></i>: 
<font color="Maroon" title="c19">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c20">m</font>
 <b>and </b><br/><a NAME="E4:70_1_1_1_1"/><i><font color="Green" title="E52">A13</font></i>: 
<font color="Maroon" title="c20">m</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c15">n</font>
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c21">m</font> = <font color="Maroon" title="c20">m</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">Y</font> ;<br/>
<a NAME="E6:70_1_1_1_1"/><i><font color="Green" title="E53">A14</font></i>: 
<font color="Maroon" title="c11">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c21">m</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c14">j</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E6:70_1_1_1"><i><font color="Green" title="E50">A11</font></i></a>, <a class="txt" href="waybel11.html#E4:70_1_1_1_1"><i><font color="Green" title="E52">A13</font></i></a></i>;<br/>
<a NAME="E7:70_1_1_1_1"/>
<font color="Maroon" title="c19">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c21">m</font></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel11.html#E17:70_1_1"><i><font color="Green" title="E47">A8</font></i></a>, <a class="txt" href="waybel11.html#E3:70_1_1_1_1"><i><font color="Green" title="E51">A12</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>;<br/>
<b>hence </b><a NAME="E8:70_1_1_1_1"/>
<font color="Maroon" title="c19">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c3">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">N</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c14">j</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="waybel11.html#E6:70_1_1_1_1"><i><font color="Green" title="E53">A14</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E9:70_1_1_1"/>
<font color="Maroon" title="c12">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">b</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E3:70_1_1_1"><i><font color="Green" title="E49">A10</font></i></a>, <a class="ref" href="waybel_7.html#T3" title="WAYBEL_7:th.3">WAYBEL_7:3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E20:70_1_1"/><b>then </b>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <font color="Maroon" title="c9">X1</font>,<font color="Maroon" title="c1">R</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <font color="Maroon" title="c10">X2</font>,<font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="ref" href="waybel11.html#T2" target="_self" title="WAYBEL11:th.2">Th2</a></i>;<br/>
<a NAME="E21:70_1_1"/><b>then </b>
<font color="Maroon" title="c6">p</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="waybel11.html#K1" title="WAYBEL11:func.1">lim_inf</a> <font color="Maroon" title="c4">Y</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E15:70_1_1"><i><font color="Green" title="E46">A7</font></i></a>, <a class="ref" href="yellow_0.html#D2" title="YELLOW_0:def.2">YELLOW_0:def 2</a></i>;<br/>
<a NAME="E22:70_1_1"/><b>then </b>
<font color="Maroon" title="c6">p</font> <a href="waybel11.html#R1" title="WAYBEL11:pred.1">is_S-limit_of</a> <font color="Maroon" title="c5">Y'</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E4:70_1_1"><i><font color="Green" title="E42">A3</font></i></a>, <a class="ref" href="waybel11.html#D7" target="_self" title="WAYBEL11:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E23:70_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">Y</font>,<font color="Maroon" title="c6">p</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E2:70_1_1"><i><font color="Green" title="E41">A2</font></i></a>, <a class="txt" href="waybel11.html#E4:70_1_1"><i><font color="Green" title="E42">A3</font></i></a>, <a class="ref" href="waybel11.html#D8" target="_self" title="WAYBEL11:def.8">Def8</a></i>;<br/>


</div>
