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

<b>let </b><font color="Maroon" title="c1">R</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<b>set </b><font color="Maroon" title="c2">IR</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>;<br/>
<b>set </b><font color="Maroon" title="c3">CR</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>;<br/>
<b>set </b><font color="Maroon" title="c4">IR'</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c5">CR'</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:34_1"/>
<font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a>  is <a href="wellfnd1.html#V1" title="WELLFND1:attr.1">well_founded</a>
 ;<br/><a NAME="E2:34_1"/><b>then </b><i><font color="Green" title="E20">A1</font></i>: 
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <a href="wellord1.html#R1" title="WELLORD1:pred.1">is_well_founded_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span>
 <b>by </b><i><a class="ref" href="wellfnd1.html#D2" title="WELLFND1:def.2">WELLFND1:def 2</a></i>;<br/><b>let </b><font color="Maroon" title="c6">N</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>;<br/><b>assume </b><a NAME="E3:34_1"/><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c6">N</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> 
 ;<br/><b>reconsider </b><font color="Maroon" title="c7">N'</font> = <font color="Maroon" title="c6">N</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> ;<br/><b>consider </b><font color="Maroon" title="c8">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:34_1"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">N'</font>
 <b>and </b><br/><a NAME="E7:34_1"/><i><font color="Green" title="E23">A4</font></i>: 
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c8">y</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c7">N'</font>
 <b>by </b><i><a class="txt" href="dickson.html#E2:34_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="dickson.html#E3:34_1"><i><font color="Green" title="E21">A2</font></i></a>, <a class="ref" href="wellord1.html#D3" title="WELLORD1:def.3">WELLORD1:def 3</a></i>;<br/><a NAME="E8:34_1"/><i><font color="Green" title="E24">A5</font></i>: 
<span class="p1">(<span class="default">the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c8">y</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c7">N'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="dickson.html#E7:34_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">y</font> = <font color="Maroon" title="c8">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <b>by </b><i><a class="txt" href="dickson.html#E6:34_1"><i><font color="Green" title="E22">A3</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c10">x</font> = <span class="p1">(<span class="default"><a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p2">(<span class="default"><a href="dickson.html#K1" title="DICKSON:func.1">EqRel</a> <font color="Maroon" title="c1">R</font></span>)</span>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c6">N</font>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:34_1_1"/>
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font>
 <b>by </b><i><a class="txt" href="dickson.html#E6:34_1"><i><font color="Green" title="E22">A3</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_1_1_1"/>
 ex <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font> &amp; <font color="Olive" title="b1">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">y</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">z</font>,<font color="Maroon" title="c9">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> )
 ;<br/><b>then consider </b><font color="Maroon" title="c11">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:34_1_1_1"/><i><font color="Green" title="E25">A6</font></i>: 
( <font color="Maroon" title="c11">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font> &amp; <font color="Maroon" title="c11">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">y</font> )
 <b>and </b><br/><a NAME="E4:34_1_1_1"/><i><font color="Green" title="E26">A7</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">z</font>,<font color="Maroon" title="c9">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span>
 ;<br/><a NAME="E5:34_1_1_1"/>
<font color="Maroon" title="c11">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c9">y</font>
 <b>by </b><i><a class="txt" href="dickson.html#E3:34_1_1_1"><i><font color="Green" title="E25">A6</font></i></a>, <a class="txt" href="dickson.html#E4:34_1_1_1"><i><font color="Green" title="E26">A7</font></i></a>, <a class="ref" href="wellord1.html#D1" title="WELLORD1:def.1">WELLORD1:def 1</a></i>;<br/><b>hence </b><a NAME="E6:34_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="dickson.html#E8:34_1"><i><font color="Green" title="E24">A5</font></i></a>, <a class="txt" href="dickson.html#E3:34_1_1_1"><i><font color="Green" title="E25">A6</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:34_1_1"/>
for <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font> or  not <font color="Olive" title="b1">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">y</font> or  not <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">z</font>,<font color="Maroon" title="c9">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> )
 ;<br/></div><b>end;</b></div><a NAME="E11:34_1"/><b>then </b>
<font color="Maroon" title="c9">y</font> <a href="waybel_4.html#R4" title="WAYBEL_4:pred.4">is_minimal_wrt</a> <font color="Maroon" title="c6">N</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span>
 <b>by </b><i><a class="ref" href="waybel_4.html#D26" title="WAYBEL_4:def.26">WAYBEL_4:def 26</a></i>;<br/><a NAME="E12:34_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p2">(<span class="default"><a href="dickson.html#K1" title="DICKSON:func.1">EqRel</a> <font color="Maroon" title="c1">R</font></span>)</span>,<font color="Maroon" title="c9">y</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c6">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dickson.html#K6" title="DICKSON:func.6">min-classes</a> <font color="Maroon" title="c6">N</font>
 <b>by </b><i><a class="ref" href="dickson.html#D8" target="_self" title="DICKSON:def.8">Def8</a></i>;<br/><b>hence </b><a NAME="E13:34_1"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dickson.html#K6" title="DICKSON:func.6">min-classes</a> <font color="Maroon" title="c6">N</font>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:34"/><i><font color="Green" title="E20">A8</font></i>: 
for <font color="Olive" title="b1">N</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b1">N</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>  holds <br/> ex <font color="Olive" title="b2">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dickson.html#K6" title="DICKSON:func.6">min-classes</a> <font color="Olive" title="b1">N</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">N</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:34_2"/><i><font color="Green" title="E21">A9</font></i>: 
<font color="Maroon" title="c6">N</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"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span>
 <b>and </b><br/><a NAME="E2:34_2"/><i><font color="Green" title="E22">A10</font></i>: 
<font color="Maroon" title="c6">N</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> 
 ;<br/><b>reconsider </b><font color="Maroon" title="c7">N'</font> = <font color="Maroon" title="c6">N</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="txt" href="dickson.html#E1:34_2"><i><font color="Green" title="E21">A9</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c8">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:34_2"/><i><font color="Green" title="E23">A11</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dickson.html#K6" title="DICKSON:func.6">min-classes</a> <font color="Maroon" title="c7">N'</font>
 <b>by </b><i><a class="txt" href="dickson.html#E2:34"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="dickson.html#E2:34_2"><i><font color="Green" title="E22">A10</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c9">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span><b> such that </b><br/><a NAME="E7:34_2"/><i><font color="Green" title="E24">A12</font></i>: 
<font color="Maroon" title="c9">a</font> <a href="waybel_4.html#R4" title="WAYBEL_4:pred.4">is_minimal_wrt</a> <font color="Maroon" title="c7">N'</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span>
 <b>and </b><br/><a NAME="E8:34_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K7" title="EQREL_1:func.7">Class</a> <span class="p2">(<span class="default"><a href="dickson.html#K1" title="DICKSON:func.1">EqRel</a> <font color="Maroon" title="c1">R</font></span>)</span>,<font color="Maroon" title="c9">a</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c7">N'</font>
 <b>by </b><i><a class="txt" href="dickson.html#E5:34_2"><i><font color="Green" title="E23">A11</font></i></a>, <a class="ref" href="dickson.html#D8" target="_self" title="DICKSON:def.8">Def8</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c10">a'</font> = <font color="Maroon" title="c9">a</font> as    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/><b>take </b><font color="Maroon" title="c11">a'</font> = <font color="Maroon" title="c10">a'</font>;<br/><b>thus </b><a NAME="E10:34_2"/>
<font color="Maroon" title="c11">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font>
 <b>by </b><i><a class="txt" href="dickson.html#E7:34_2"><i><font color="Green" title="E24">A12</font></i></a>, <a class="ref" href="waybel_4.html#D26" title="WAYBEL_4:def.26">WAYBEL_4:def 26</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2_1"/>
<span class="p1">(<span class="default">the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c11">a'</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c6">N</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> 
 ;<br/><b>then consider </b><font color="Maroon" title="c12">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:34_2_1"/><i><font color="Green" title="E25">A13</font></i>: 
<font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default">the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c11">a'</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c6">N</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/><a NAME="E4:34_2_1"/><i><font color="Green" title="E26">A14</font></i>: 
( <font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c11">a'</font> &amp; <font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font> )
 <b>by </b><i><a class="txt" href="dickson.html#E3:34_2_1"><i><font color="Green" title="E25">A13</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c13">z</font> = <font color="Maroon" title="c12">z</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <b>by </b><i><a class="txt" href="dickson.html#E1:34_2"><i><font color="Green" title="E21">A9</font></i></a></i>;<br/><a NAME="E6:34_2_1"/>
( <font color="Maroon" title="c13">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a'</font> &amp; <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Maroon" title="c13">z</font>,<font color="Maroon" title="c9">a</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="dickson.html#E4:34_2_1"><i><font color="Green" title="E26">A14</font></i></a>, <a class="ref" href="wellord1.html#D1" title="WELLORD1:def.1">WELLORD1:def 1</a></i>;<br/><b>hence </b><a NAME="E7:34_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="dickson.html#E7:34_2"><i><font color="Green" title="E24">A12</font></i></a>, <a class="txt" href="dickson.html#E4:34_2_1"><i><font color="Green" title="E26">A14</font></i></a>, <a class="ref" href="waybel_4.html#D26" title="WAYBEL_4:def.26">WAYBEL_4:def 26</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E12:34_2"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c11">a'</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c6">N</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:34"/><b>then </b>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span> <a href="wellord1.html#R1" title="WELLORD1:pred.1">is_well_founded_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="wellord1.html#D3" title="WELLORD1:def.3">WELLORD1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:34"/>
<font color="Maroon" title="c1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a>  is <a href="wellfnd1.html#V1" title="WELLFND1:attr.1">well_founded</a>
 <b>by </b><i><a class="ref" href="wellfnd1.html#D2" title="WELLFND1:def.2">WELLFND1:def 2</a></i>;<br/>


</div>
