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

<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/><b>let </b><font color="Maroon" title="c2">F</font> be  <a href="waybel_7.html#V3" title="WAYBEL_7:attr.3">ultra</a> <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>;<br/><b>let </b><font color="Maroon" title="c3">p</font> be  <a href="waybel28.html#V1" title="WAYBEL28:attr.1">greater_or_equal_to_id</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span>;<br/>





<b>set </b><font color="Maroon" title="c4">M</font> = <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font>;<br/>
<a NAME="E1:29"/><i><font color="Green" title="E20">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel28.html#T7" title="WAYBEL28:th.7">WAYBEL28:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">g</font> = <font color="Maroon" title="c3">p</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> ;<br/>
<b>set </b><font color="Maroon" title="c6">rM</font> =  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c7">C</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">F</font>;<br/>
<a NAME="E4:29"/>
<font color="Maroon" title="c2">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E5:29"/><b>then </b>
<font color="Maroon" title="c2">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_7.html#T4" title="WAYBEL_7:th.4">WAYBEL_7:4</a></i>;<br/>
<a NAME="E6:29"/><b>then </b>
<font color="Maroon" title="c7">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E7:29"/><b>then </b><i><font color="Green" title="E21">A2</font></i>: 
( <font color="Maroon" title="c7">C</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Maroon" title="c7">C</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c8">D</font> = <font color="Maroon" title="c7">C</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span>, <font color="Maroon" title="c9">A</font> = <font color="Maroon" title="c7">C</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="waybel_7.html#T4" title="WAYBEL_7:th.4">WAYBEL_7:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">A'</font> = <font color="Maroon" title="c9">A</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<a NAME="E10:29"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c2">F</font> is <a href="waybel_7.html#V2" title="WAYBEL_7:attr.2">prime</a>
 
<b>by </b><i><a class="ref" href="waybel_7.html#T26" title="WAYBEL_7:th.26">WAYBEL_7:26</a></i>;<br/>
<i><font color="Green" title="E23">A4</font></i>: <font color="Maroon" title="c8">D</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c9">A</font> = 
<font color="Maroon" title="c8">D</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c9">A</font>
<b>by </b><i><a class="ref" href="yellow_1.html#T17" title="YELLOW_1:th.17">YELLOW_1:17</a></i>
<br/>.= 
<font color="Maroon" title="c7">C</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T51" title="XBOOLE_1:th.51">XBOOLE_1:51</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:29_2"/><i><font color="Green" title="E24">A5</font></i>: 
<font color="Maroon" title="c8">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font>
 ;<br/><b>consider </b><font color="Maroon" title="c11">d</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c8">D</font>;<br/><a NAME="E3:29_2"/>
not  <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K3" title="YELLOW_1:func.3">BoolePoset</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font>
 <b>by </b><i><a class="ref" href="waybel_7.html#T8" title="WAYBEL_7:th.8">WAYBEL_7:8</a></i>;<br/><a NAME="E4:29_2"/><b>then </b><i><font color="Green" title="E25">A6</font></i>: 
<font color="Maroon" title="c8">D</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="waybel33.html#E1:29_2"><i><font color="Green" title="E24">A5</font></i></a>, <a class="ref" href="yellow_1.html#T18" title="YELLOW_1:th.18">YELLOW_1:18</a></i>;<br/><a NAME="E5:29_2"/><b>then </b>
<font color="Maroon" title="c11">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">D</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c12">d</font> = <font color="Maroon" title="c11">d</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="waybel33.html#E7:29"><i><font color="Green" title="E21">A2</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">D</font> = <font color="Maroon" title="c8">D</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">F</font> <b>by </b><i><a class="txt" href="waybel33.html#E1:29_2"><i><font color="Green" title="E24">A5</font></i></a></i>;<br/><a NAME="E8:29_2"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">D</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>, <font color="Olive" title="b2">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">F</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">f</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="waybel33.html#E4:29_2"><i><font color="Green" title="E25">A6</font></i></a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c14">dD</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">D</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <b>by </b><i><a class="ref" href="yellow19.html#D4" title="YELLOW19:def.4">YELLOW19:def 4</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c15">dD'</font> = <font color="Maroon" title="c14">dD</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <b>by </b><i><a class="ref" href="waybel28.html#T7" title="WAYBEL28:th.7">WAYBEL28:7</a></i>;<br/><a NAME="E11:29_2"/>
 ex <font color="Olive" title="b1">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span> st <br/>for <font color="Olive" title="b2">j</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>  st <font color="Olive" title="b2">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">i</font> holds <br/><font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Olive" title="b2">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c14">dD</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c16">i</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span><b> such that </b><br/><a NAME="E2:29_2_1"/><i><font color="Green" title="E26">A7</font></i>: 
<font color="Maroon" title="c16">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">dD'</font>
 ;<br/>
<a NAME="E3:29_2_1"/><i><font color="Green" title="E27">A8</font></i>: 
for <font color="Olive" title="b1">j</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>  st <font color="Olive" title="b1">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">i</font> holds <br/><font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Olive" title="b1">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c14">dD</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c17">j</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:29_2_1_1"/><i><font color="Green" title="E28">A9</font></i>: 
<font color="Maroon" title="c17">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">i</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c18">j'</font> = <font color="Maroon" title="c17">j</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <b>by </b><i><a class="ref" href="waybel28.html#T7" title="WAYBEL28:th.7">WAYBEL28:7</a></i>;<br/>
<a NAME="E3:29_2_1_1"/><i><font color="Green" title="E29">A10</font></i>: 
<font color="Maroon" title="c18">j'</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c17">j</font>
 
<b>by </b><i><a class="ref" href="waybel28.html#D1" title="WAYBEL28:def.1">WAYBEL28:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c19">j'</font> = <font color="Maroon" title="c18">j'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c20">i'</font> = <font color="Maroon" title="c16">i</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <b>by </b><i><a class="ref" href="waybel28.html#T7" title="WAYBEL28:th.7">WAYBEL28:7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c21">i'</font> = <font color="Maroon" title="c20">i'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> ;<br/>
<a NAME="E7:29_2_1_1"/>
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="waybel28.html#D2" title="WAYBEL28:def.2">WAYBEL28:def 2</a></i>;<br/>
<a NAME="E8:29_2_1_1"/><b>then </b>
<font color="Maroon" title="c21">i'</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c19">j'</font>
 
<b>by </b><i><a class="txt" href="waybel33.html#E1:29_2_1_1"><i><font color="Green" title="E28">A9</font></i></a>, <a class="ref" href="yellow_0.html#T1" title="YELLOW_0:th.1">YELLOW_0:1</a></i>;<br/>
<b>hence </b><a NAME="E9:29_2_1_1"/>
<font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c17">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c14">dD</font>
 <b>by </b><i><a class="txt" href="waybel33.html#E2:29_2_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="txt" href="waybel33.html#E3:29_2_1_1"><i><font color="Green" title="E29">A10</font></i></a>, <a class="ref" href="yellow_0.html#D2" title="YELLOW_0:def.2">YELLOW_0:def 2</a></i>;<br/>


</div><b>end;</b></div>
<b>take </b>
<font color="Maroon" title="c16">i</font>
;<br/>

<b>thus </b><a NAME="E4:29_2_1"/>
for <font color="Olive" title="b1">j</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>  st <font color="Olive" title="b1">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">i</font> holds <br/><font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Olive" title="b1">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c14">dD</font>
 <b>by </b><i><a class="txt" href="waybel33.html#E3:29_2_1"><i><font color="Green" title="E27">A8</font></i></a></i>;<br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c16">i</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span><b> such that </b><br/><a NAME="E13:29_2"/><i><font color="Green" title="E26">A11</font></i>: 
for <font color="Olive" title="b1">j</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>  st <font color="Olive" title="b1">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">i</font> holds <br/><font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Olive" title="b1">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c14">dD</font>
 ;<br/><a NAME="E14:29_2"/>
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> #)
 <b>by </b><i><a class="ref" href="waybel28.html#D2" title="WAYBEL28:def.2">WAYBEL28:def 2</a></i>;<br/><a NAME="E15:29_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font> is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>
 <b>by </b><i><a class="ref" href="waybel_8.html#T12" title="WAYBEL_8:th.12">WAYBEL_8:12</a></i>;<br/><a NAME="E16:29_2"/><b>then </b>
<font color="Maroon" title="c16">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">i</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D1" title="YELLOW_0:def.1">YELLOW_0:def 1</a></i>;<br/><a NAME="E17:29_2"/><b>then </b><i><font color="Green" title="E27">A12</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c16">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c14">dD</font>
 <b>by </b><i><a class="txt" href="waybel33.html#E13:29_2"><i><font color="Green" title="E26">A11</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c17">G</font> = <font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c16">i</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> ;<br/><a NAME="E19:29_2"/>
<font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c16">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span>
 ;<br/><a NAME="E20:29_2"/><b>then </b>
<font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c16">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>, <font color="Olive" title="b2">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">F</font> : <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">f</font> </span>}</span> 
 <b>by </b><i><a class="ref" href="yellow19.html#D4" title="YELLOW19:def.4">YELLOW19:def 4</a></i>;<br/><b>then consider </b><font color="Maroon" title="c18">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>, <font color="Maroon" title="c19">f</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">F</font><b> such that </b><br/><a NAME="E22:29_2"/><i><font color="Green" title="E28">A13</font></i>: 
( <font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c16">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">a</font>,<font color="Maroon" title="c19">f</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp; <font color="Maroon" title="c18">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">f</font> )
 ;<br/><a NAME="E23:29_2"/><i><font color="Green" title="E29">A14</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c16">i</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">a</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c16">i</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">f</font> )
 <b>by </b><i><a class="txt" href="waybel33.html#E22:29_2"><i><font color="Green" title="E28">A13</font></i></a>, <a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><a NAME="E24:29_2"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="yellow_6.html#K3" title="YELLOW_6:func.3">.</a> <font color="Maroon" title="c16">i</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  &amp; <font color="Maroon" title="c14">dD</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">D</font> )
 <b>by </b><i><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></i>;<br/><a NAME="E25:29_2"/><b>then </b><i><font color="Green" title="E30">A15</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">D</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  )
 <b>by </b><i><a class="txt" href="waybel33.html#E17:29_2"><i><font color="Green" title="E27">A12</font></i></a>, <a class="txt" href="waybel33.html#E22:29_2"><i><font color="Green" title="E28">A13</font></i></a>, <a class="txt" href="waybel33.html#E23:29_2"><i><font color="Green" title="E29">A14</font></i></a>, <a class="ref" href="yellow19.html#D4" title="YELLOW19:def.4">YELLOW19:def 4</a></i>;<br/><a NAME="E26:29_2"/><i><font color="Green" title="E31">A16</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T67" title="FUNCT_2:th.67">FUNCT_2:67</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c16">i</font> = 
<span class="p1">(<span class="default">the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font>
<b>by </b><i><a class="ref" href="waybel28.html#D2" title="WAYBEL28:def.2">WAYBEL28:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c17">G</font>
<b>by </b><i><a class="txt" href="waybel33.html#E1:29"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="waybel33.html#E26:29_2"><i><font color="Green" title="E31">A16</font></i></a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">i</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<b>by </b><i><a class="ref" href="yellow19.html#D4" title="YELLOW19:def.4">YELLOW19:def 4</a></i>
;<br/><a NAME="E28:29_2"/><b>then </b>
not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c16">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel33.html#E25:29_2"><i><font color="Green" title="E30">A15</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><b>hence </b><a NAME="E29:29_2"/>
contradiction
 <b>by </b><i><a class="ref" href="funct_2.html#T6" title="FUNCT_2:th.6">FUNCT_2:6</a></i>;<br/></div><b>end;</b></div>
<a NAME="E13:29"/><b>then </b><i><font color="Green" title="E24">A17</font></i>: 
( <font color="Maroon" title="c9">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span> &amp; <font color="Maroon" title="c9">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> )
 
<b>by </b><i><a class="txt" href="waybel33.html#E10:29"><i><font color="Green" title="E22">A3</font></i></a>, <a class="txt" href="waybel33.html#E11:29"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="waybel_7.html#D2" title="WAYBEL_7:def.2">WAYBEL_7:def 2</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
 <a href="waybel_9.html#K2" title="WAYBEL_9:func.2">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span> = 
 <a href="yellow_2.html#NK7" title="YELLOW_2:NK.7">Inf</a> 
<b>by </b><i><a class="ref" href="waybel_9.html#D2" title="WAYBEL_9:def.2">WAYBEL_9:def 2</a></i>
<br/>.= 
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span></span>)</span>,<font color="Maroon" title="c1">L</font>
<b>by </b><i><a class="ref" href="yellow_2.html#D6" title="YELLOW_2:def.6">YELLOW_2:def 6</a></i>
;<br/>
<a NAME="E15:29"/><b>then </b><i><font color="Green" title="E25">A18</font></i>: 
 <a href="waybel_9.html#K2" title="WAYBEL_9:func.2">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Maroon" title="c10">A'</font>
 
<b>by </b><i><a class="txt" href="waybel33.html#E13:29"><i><font color="Green" title="E24">A17</font></i></a>, <a class="ref" href="waybel_7.html#T3" title="WAYBEL_7:th.3">WAYBEL_7:3</a></i>;<br/>
<b>set </b><font color="Maroon" title="c11">Y</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> : <font color="Olive" title="b1">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> </span>}</span> ;<br/>
<a NAME="E16:29"/><i><font color="Green" title="E26">A19</font></i>: 
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Maroon" title="c10">A'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> : <font color="Olive" title="b1">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="waybel33.html#E13:29"><i><font color="Green" title="E24">A17</font></i></a></i>;<br/>
<a NAME="E17:29"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Olive" title="b1">B</font></span>)</span> where <font color="Olive" title="b1">B</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> : <font color="Olive" title="b1">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> </span>}</span> ,<font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T17" title="YELLOW_0:th.17">YELLOW_0:17</a></i>;<br/>
<a NAME="E18:29"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Maroon" title="c10">A'</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="waybel33.html#K1" title="WAYBEL33:func.1">lim_inf</a> <font color="Maroon" title="c2">F</font>
 
<b>by </b><i><a class="txt" href="waybel33.html#E16:29"><i><font color="Green" title="E26">A19</font></i></a>, <a class="ref" href="yellow_4.html#T1" title="YELLOW_4:th.1">YELLOW_4:1</a></i>;<br/>
<b>hence </b><a NAME="E19:29"/>
 <a href="waybel33.html#K1" title="WAYBEL33:func.1">lim_inf</a> <font color="Maroon" title="c2">F</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a>  <a href="waybel_9.html#K2" title="WAYBEL_9:func.2">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3" title="YELLOW19:func.3">a_net</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="waybel28.html#K2" title="WAYBEL28:func.2">*</a> <font color="Maroon" title="c3">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel33.html#E15:29"><i><font color="Green" title="E25">A18</font></i></a>, <a class="ref" href="yellow_0.html#D2" title="YELLOW_0:def.2">YELLOW_0:def 2</a></i>;<br/>


</div>
