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

<span class="kw">set </span><font color="Maroon" title="c1">IR9</font> =  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c2">CR9</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_2_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">N</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">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"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a></span>)</span> &amp; <font color="Maroon" title="c3">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>  implies  ex <font color="Olive" title="b1">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp;  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <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="Olive" title="b1">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">N</font> ) )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:72_2_1_1"/><span class="lab"><font color="Green" title="E51">A1</font></span>: 
<font color="Maroon" title="c3">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"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:72_2_1_1"/><span class="lab"><font color="Green" title="E52">A2</font></span>: 
<font color="Maroon" title="c3">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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp;  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <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="Olive" title="b1">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">N</font> )</span><br/><a NAME="E3:72_2_1_1"/><span class="lab"><font color="Green" title="E53">A3</font></span>: 
 ex <font color="Olive" title="b1">k</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:72_2_1_1"><span class="lab"><font color="Green" title="E52">A2</font></span></a>, <a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></span>;<br/><span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span><font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font>;<br/><a NAME="E4:72_2_1_1"/><span class="lab"><font color="Green" title="E54">A4</font></span>: 
 ex <font color="Olive" title="b1">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72_2_1_1"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="txt" href="#E3:72_2_1_1"><span class="lab"><font color="Green" title="E53">A3</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c4">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E6:72_2_1_1"/><span class="lab"><font color="Green" title="E55">A5</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">m</font>]
 <span class="kw">and </span><br/><a NAME="E7:72_2_1_1"/><span class="lab"><font color="Green" title="E56">A6</font></span>: 
 for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon" title="c4">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font>
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S5" title="NAT_1:sch.5">NAT_1:sch 5</a>(<a class="txt" href="#E4:72_2_1_1"><span class="lab"><font color="Green" title="E54">A4</font></span></a>);<br/></span><span class="kw">reconsider </span><font color="Maroon" title="c5">m</font> = <font color="Maroon" title="c4">m</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/><span class="kw">thus </span><a NAME="E9:72_2_1_1"/>
 ex <font color="Olive" title="b1">m</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp;  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <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="Olive" title="b1">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">N</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_2_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">take </span>
<font color="Maroon" title="c5">m</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> &amp;  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <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="c5">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">N</font> )</span><br/>

<span class="kw">thus </span><a NAME="E1:72_2_1_1_1"/>
<font color="Maroon" title="c5">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:72_2_1_1"><span class="lab"><font color="Green" title="E55">A5</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <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="c5">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">N</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_2_1_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:72_2_1_1_1_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"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <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="c5">m</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:72_2_1_1_1_1"/><span class="lab"><font color="Green" title="E57">A7</font></span>: 
<font color="Maroon" title="c6">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"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <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="c5">m</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></span>;<br/><a NAME="E4:72_2_1_1_1_1"/><span class="lab"><font color="Green" title="E58">A8</font></span>: 
<font color="Maroon" title="c6">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"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <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="c5">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E57">A7</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E5:72_2_1_1_1_1"/><span class="lab"><font color="Green" title="E59">A9</font></span>: 
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E57">A7</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E6:72_2_1_1_1_1"/><span class="lab"><font color="Green" title="E60">A10</font></span>: 
<font color="Maroon" title="c6">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E58">A8</font></span></a>, <a class="ref" href="wellord1.html#T1" title="WELLORD1:th.1">WELLORD1:1</a></span>;<br/><a NAME="E7:72_2_1_1_1_1"/><span class="lab"><font color="Green" title="E61">A11</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">m</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"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E58">A8</font></span></a>, <a class="ref" href="wellord1.html#T1" title="WELLORD1:th.1">WELLORD1:1</a></span>;<br/><a NAME="E8:72_2_1_1_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">m</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="dickson.html#K10" title="DICKSON:func.10">NATOrd</a> 
 ;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c8">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E10:72_2_1_1_1_1"/><span class="lab"><font color="Green" title="E62">A12</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">z</font>,<font color="Maroon" title="c5">m</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <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="c7">x</font>,<font color="Maroon" title="c8">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <span class="kw">and </span><br/><a NAME="E11:72_2_1_1_1_1"/>
<font color="Maroon" title="c7">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">y</font>
 ;<br/><a NAME="E12:72_2_1_1_1_1"/><span class="lab"><font color="Green" title="E63">A13</font></span>: 
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E62">A12</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/><a NAME="E13:72_2_1_1_1_1"/><span class="lab"><font color="Green" title="E64">A14</font></span>: 
<font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E62">A12</font></span></a>, <a class="ref" href="zfmisc_1.html#T27" title="ZFMISC_1:th.27">ZFMISC_1:27</a></span>;<br/><a NAME="E14:72_2_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:72_2_1_1"><span class="lab"><font color="Green" title="E56">A6</font></span></a>, <a class="txt" href="#E5:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E59">A9</font></span></a>, <a class="txt" href="#E12:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E63">A13</font></span></a></span>;<br/><a NAME="E15:72_2_1_1_1_1"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">y</font>,<font color="Maroon" title="c7">x</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>  <a href="dickson.html#K10" title="DICKSON:func.10">NATOrd</a> 
 ;<br/><span class="kw">hence </span><a NAME="E16:72_2_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E60">A10</font></span></a>, <a class="txt" href="#E7:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E61">A11</font></span></a>, <a class="txt" href="#E12:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E63">A13</font></span></a>, <a class="txt" href="#E13:72_2_1_1_1_1"><span class="lab"><font color="Green" title="E64">A14</font></span></a>, <a class="ref" href="dickson.html#T44" target="_self" title="DICKSON:th.44">Th45</a>, <a class="ref" href="relat_2.html#D4" title="RELAT_2:def.4">RELAT_2:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:72_2_1_1_1"/>
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <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="c5">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<a NAME="E2:72_2_1"/><span class="kw">then </span>
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <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"><a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="wellord1.html#D3" title="WELLORD1:def.3">WELLORD1:def 3</a></span>;<br/>
<a NAME="E3:72_2_1"/><span class="kw">then </span>
<a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a>  is  <a href="wellfnd1.html#V1" title="WELLFND1:attr.1">well_founded</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="wellfnd1.html#D2" title="WELLFND1:def.2">WELLFND1:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:72_2_1"/>
 <a href="dickson.html#K11" title="DICKSON:func.11">OrderedNAT</a>  is  <a href="dickson.html#V4" title="DICKSON:attr.4">Dickson</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="dickson.html#T27" target="_self" title="DICKSON:th.27">Th28</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
