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

<b>let </b><font color="Maroon" title="c1">o</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/>

<b>set </b><font color="Maroon" title="c2">gilo</font> =  <a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font>;<br/>
<b>set </b><font color="Maroon" title="c3">ilo</font> =  <a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font>;<br/>
<a NAME="E1:51"/><i><font color="Green" title="E30">A1</font></i>: 
 <a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font> <a href="relat_2.html#R7" title="RELAT_2:pred.7">is_strongly_connected_in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font>
 
<b>by </b><i><a class="ref" href="bagorder.html#D7" target="_self" title="BAGORDER:def.7">Def7</a></i>;<br/>
<a NAME="E2:51"/><i><font color="Green" title="E31">A2</font></i>: 
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font>
 
<b>by </b><i><a class="ref" href="orders_1.html#T97" title="ORDERS_1:th.97">ORDERS_1:97</a></i>;<br/>
<a NAME="E3:51"/><b>then </b><i><font color="Green" title="E32">A3</font></i>: 
 <a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D9" title="RELAT_2:def.9">RELAT_2:def 9</a></i>;<br/>
<a NAME="E4:51"/><i><font color="Green" title="E33">A4</font></i>: 
 <a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font>
 
<b>by </b><i><a class="txt" href="bagorder.html#E2:51"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="relat_2.html#D16" title="RELAT_2:def.16">RELAT_2:def 16</a></i>;<br/>
<a NAME="E5:51"/><i><font color="Green" title="E34">A5</font></i>: 
 <a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font> <a href="relat_2.html#R4" title="RELAT_2:pred.4">is_antisymmetric_in</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font>
 
<b>by </b><i><a class="txt" href="bagorder.html#E2:51"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="relat_2.html#D12" title="RELAT_2:def.12">RELAT_2:def 12</a></i>;<br/>
<a NAME="E6:51"/><i><font color="Green" title="E35">A6</font></i>: 
 <a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font> <a href="relat_2.html#R6" title="RELAT_2:pred.6">is_connected_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bagorder.html#E1:51"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="bagorder.html#E2:51"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="orders_1.html#T92" title="ORDERS_1:th.92">ORDERS_1:92</a></i>;<br/>
<a NAME="E7:51"/><i><font color="Green" title="E36">A7</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">o</font>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</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="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Olive" title="b3">c</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Olive" title="b3">c</font></span>)</span></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="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font>
 
<b>by </b><i><a class="ref" href="bagorder.html#D7" target="_self" title="BAGORDER:def.7">Def7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:51_1"/><i><font color="Green" title="E37">A8</font></i>: 
<font color="Maroon" title="c4">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span>
 <b>and </b><br/><a NAME="E2:51_1"/><i><font color="Green" title="E38">A9</font></i>: 
<font color="Maroon" title="c4">Y</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>set </b><font color="Maroon" title="c5">TD</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font></span>)</span> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> </span>}</span> ;<br/><b>consider </b><font color="Maroon" title="c6">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:51_1"/><i><font color="Green" title="E39">A10</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font>
 <b>by </b><i><a class="txt" href="bagorder.html#E2:51_1"><i><font color="Green" title="E38">A9</font></i></a>, <a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c7">x</font> = <font color="Maroon" title="c6">x</font> as    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> <b>by </b><i><a class="txt" href="bagorder.html#E1:51_1"><i><font color="Green" title="E37">A8</font></i></a>, <a class="txt" href="bagorder.html#E4:51_1"><i><font color="Green" title="E39">A10</font></i></a>, <a class="ref" href="orders_1.html#T97" title="ORDERS_1:th.97">ORDERS_1:97</a></i>;<br/><a NAME="E6:51_1"/><i><font color="Green" title="E40">A11</font></i>: 
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c7">x</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="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font></span>)</span> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> </span>}</span> 
 <b>by </b><i><a class="txt" href="bagorder.html#E4:51_1"><i><font color="Green" title="E39">A10</font></i></a></i>;<br/><a NAME="E7:51_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font></span>)</span> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</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="E1:51_1_1"/>
<font color="Maroon" title="c8">x</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="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font></span>)</span> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c9">y</font> being    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font><b> such that </b><br/><a NAME="E3:51_1_1"/><i><font color="Green" title="E41">A12</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c9">y</font>
 <b>and </b><br/><a NAME="E4:51_1_1"/>
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font>
 ;<br/>
<b>thus </b><a NAME="E5:51_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="txt" href="bagorder.html#E3:51_1_1"><i><font color="Green" title="E41">A12</font></i></a></i>;<br/>


</div><b>end;</b></div><b>then reconsider </b><font color="Maroon" title="c8">TD</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font></span>)</span> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> </span>}</span>  as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="bagorder.html#E6:51_1"><i><font color="Green" title="E40">A11</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c9">mTD</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> &amp;  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font> ) </span>}</span> ;<br/><a NAME="E9:51_1"/><i><font color="Green" title="E41">A13</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> &amp;  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font> ) </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">x</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="E1:51_1_2"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> &amp;  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font> ) </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c11">y</font> being    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font><b> such that </b><br/><a NAME="E3:51_1_2"/><i><font color="Green" title="E42">A14</font></i>: 
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">y</font>
 <b>and </b><br/><a NAME="E4:51_1_2"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font>
 <b>and </b><br/><a NAME="E5:51_1_2"/>
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font>
 ;<br/>
<b>thus </b><a NAME="E6:51_1_2"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span>
 <b>by </b><i><a class="txt" href="bagorder.html#E2:51"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="bagorder.html#E3:51_1_2"><i><font color="Green" title="E42">A14</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E10:51_1"/>
 <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">TD</font>
 <b>by </b><i><a class="ref" href="cqc_sim1.html#D8" title="CQC_SIM1:def.8">CQC_SIM1:def 8</a></i>;<br/><b>then consider </b><font color="Maroon" title="c10">y</font> being    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font><b> such that </b><br/><a NAME="E12:51_1"/><i><font color="Green" title="E42">A15</font></i>: 
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font>
 <b>and </b><br/><a NAME="E13:51_1"/><i><font color="Green" title="E43">A16</font></i>: 
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font>
 ;<br/><a NAME="E14:51_1"/><i><font color="Green" title="E44">A17</font></i>: 
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> &amp;  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="bagorder.html#E12:51_1"><i><font color="Green" title="E42">A15</font></i></a>, <a class="txt" href="bagorder.html#E13:51_1"><i><font color="Green" title="E43">A16</font></i></a></i>;<br/><a NAME="E15:51_1"/><i><font color="Green" title="E45">A18</font></i>: 
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font>
 <b>by </b><i><a class="ref" href="orders_1.html#T97" title="ORDERS_1:th.97">ORDERS_1:97</a></i>;<br/><a NAME="E16:51_1"/>
 <a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>
 <b>by </b><i><a class="ref" href="bagorder.html#T26" target="_self" title="BAGORDER:th.26">Th26</a></i>;<br/><a NAME="E17:51_1"/><b>then </b>
 <a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font> <a href="wellord1.html#R2" title="WELLORD1:pred.2">well_orders</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span>
 <b>by </b><i><a class="ref" href="wellord1.html#T8" title="WELLORD1:th.8">WELLORD1:8</a></i>;<br/><a NAME="E18:51_1"/><b>then </b>
 <a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font> <a href="wellord1.html#R1" title="WELLORD1:pred.1">is_well_founded_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span>
 <b>by </b><i><a class="ref" href="wellord1.html#D5" title="WELLORD1:def.5">WELLORD1:def 5</a></i>;<br/><b>then consider </b><font color="Maroon" title="c11">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E20:51_1"/><i><font color="Green" title="E46">A19</font></i>: 
<font color="Maroon" title="c11">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> &amp;  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font> ) </span>}</span> 
 <b>and </b><br/><a NAME="E21:51_1"/><i><font color="Green" title="E47">A20</font></i>: 
<span class="p1">(<span class="default"><a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font></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> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> &amp;  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="bagorder.html#E2:51"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="bagorder.html#E9:51_1"><i><font color="Green" title="E41">A13</font></i></a>, <a class="txt" href="bagorder.html#E14:51_1"><i><font color="Green" title="E44">A17</font></i></a>, <a class="txt" href="bagorder.html#E15:51_1"><i><font color="Green" title="E45">A18</font></i></a>, <a class="ref" href="wellord1.html#D3" title="WELLORD1:def.3">WELLORD1:def 3</a></i>;<br/><a NAME="E22:51_1"/><i><font color="Green" title="E48">A21</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font></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> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> &amp;  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font> ) </span>}</span>  <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="bagorder.html#E21:51_1"><i><font color="Green" title="E47">A20</font></i></a>, <a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/><b>consider </b><font color="Maroon" title="c12">a'</font> being    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font><b> such that </b><br/><a NAME="E24:51_1"/><i><font color="Green" title="E49">A22</font></i>: 
<font color="Maroon" title="c12">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a</font>
 <b>and </b><br/><a NAME="E25:51_1"/><i><font color="Green" title="E50">A23</font></i>: 
( <font color="Maroon" title="c12">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> &amp;  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c12">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font> )
 <b>by </b><i><a class="txt" href="bagorder.html#E20:51_1"><i><font color="Green" title="E46">A19</font></i></a></i>;<br/><b>take </b><font color="Maroon" title="c13">a</font> = <font color="Maroon" title="c11">a</font>;<br/><b>thus </b><a NAME="E26:51_1"/>
<font color="Maroon" title="c13">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font>
 <b>by </b><i><a class="txt" href="bagorder.html#E24:51_1"><i><font color="Green" title="E49">A22</font></i></a>, <a class="txt" href="bagorder.html#E25:51_1"><i><font color="Green" title="E50">A23</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:51_1_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c13">a</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c4">Y</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="c14">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:51_1_3"/><i><font color="Green" title="E51">A24</font></i>: 
<font color="Maroon" title="c14">z</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="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c13">a</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c4">Y</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="E4:51_1_3"/><i><font color="Green" title="E52">A25</font></i>: 
<font color="Maroon" title="c14">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c13">a</font>
 <b>by </b><i><a class="txt" href="bagorder.html#E3:51_1_3"><i><font color="Green" title="E51">A24</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E5:51_1_3"/><i><font color="Green" title="E53">A26</font></i>: 
<font color="Maroon" title="c14">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font>
 <b>by </b><i><a class="txt" href="bagorder.html#E3:51_1_3"><i><font color="Green" title="E51">A24</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E6:51_1_3"/><i><font color="Green" title="E54">A27</font></i>: 
( <font color="Maroon" title="c14">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">a</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">z</font>,<font color="Maroon" title="c13">a</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="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font> )
 <b>by </b><i><a class="txt" href="bagorder.html#E4:51_1_3"><i><font color="Green" title="E52">A25</font></i></a>, <a class="ref" href="wellord1.html#D1" title="WELLORD1:def.1">WELLORD1:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c15">a</font> = <font color="Maroon" title="c13">a</font>, <font color="Maroon" title="c16">z</font> = <font color="Maroon" title="c14">z</font> as    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> <b>by </b><i><a class="txt" href="bagorder.html#E1:51_1"><i><font color="Green" title="E37">A8</font></i></a>, <a class="txt" href="bagorder.html#E24:51_1"><i><font color="Green" title="E49">A22</font></i></a>, <a class="txt" href="bagorder.html#E5:51_1_3"><i><font color="Green" title="E53">A26</font></i></a>, <a class="ref" href="orders_1.html#T97" title="ORDERS_1:th.97">ORDERS_1:97</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:51_1_3_1"/>
(  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c16">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c15">a</font> or  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c15">a</font> or  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c16">z</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c15">a</font> )
 </span><b>by </b><i><a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_3_1_1"><b>suppose </b></a><a NAME="E1:51_1_3_1_1"/><i><font color="Green" title="E55">A28</font></i>: 
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c16">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c15">a</font>
 ;<br/><div class="add"><a NAME="E2:51_1_3_1_1"/>
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c16">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">TD</font>
 <b>by </b><i><a class="txt" href="bagorder.html#E5:51_1_3"><i><font color="Green" title="E53">A26</font></i></a></i>;<br/><b>hence </b><a NAME="E3:51_1_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="bagorder.html#E24:51_1"><i><font color="Green" title="E49">A22</font></i></a>, <a class="txt" href="bagorder.html#E25:51_1"><i><font color="Green" title="E50">A23</font></i></a>, <a class="txt" href="bagorder.html#E1:51_1_3_1_1"><i><font color="Green" title="E55">A28</font></i></a>, <a class="ref" href="cqc_sim1.html#D8" title="CQC_SIM1:def.8">CQC_SIM1:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_3_1_2"><b>suppose </b></a><a NAME="E1:51_1_3_1_2"/><i><font color="Green" title="E55">A29</font></i>: 
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c16">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c15">a</font>
 ;<br/><div class="add"><a NAME="E2:51_1_3_1_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c16">z</font>,<font color="Maroon" title="c15">a</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="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font>
 <b>by </b><i><a class="txt" href="bagorder.html#E7:51"><i><font color="Green" title="E36">A7</font></i></a>, <a class="txt" href="bagorder.html#E6:51_1_3"><i><font color="Green" title="E54">A27</font></i></a>, <a class="ref" href="bagorder.html#D9" target="_self" title="BAGORDER:def.9">Def9</a></i>;<br/><a NAME="E3:51_1_3_1_2"/><b>then </b><i><font color="Green" title="E56">A30</font></i>: 
<font color="Maroon" title="c16">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="bagorder.html#K4" title="BAGORDER:func.4">InvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c15">a</font>
 <b>by </b><i><a class="txt" href="bagorder.html#E6:51_1_3"><i><font color="Green" title="E54">A27</font></i></a>, <a class="ref" href="wellord1.html#D1" title="WELLORD1:def.1">WELLORD1:def 1</a></i>;<br/><a NAME="E4:51_1_3_1_2"/>
<font color="Maroon" title="c16">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">o</font> : ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Y</font> &amp;  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_sim1.html#K10" title="CQC_SIM1:func.10">min</a> <font color="Maroon" title="c8">TD</font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="bagorder.html#E24:51_1"><i><font color="Green" title="E49">A22</font></i></a>, <a class="txt" href="bagorder.html#E25:51_1"><i><font color="Green" title="E50">A23</font></i></a>, <a class="txt" href="bagorder.html#E5:51_1_3"><i><font color="Green" title="E53">A26</font></i></a>, <a class="txt" href="bagorder.html#E1:51_1_3_1_2"><i><font color="Green" title="E55">A29</font></i></a></i>;<br/><b>hence </b><a NAME="E5:51_1_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="bagorder.html#E22:51_1"><i><font color="Green" title="E48">A21</font></i></a>, <a class="txt" href="bagorder.html#E3:51_1_3_1_2"><i><font color="Green" title="E56">A30</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_3_1_3"><b>suppose </b></a><a NAME="E1:51_1_3_1_3"/>
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c16">z</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c15">a</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:51_1_3_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="bagorder.html#E7:51"><i><font color="Green" title="E36">A7</font></i></a>, <a class="txt" href="bagorder.html#E6:51_1_3"><i><font color="Green" title="E54">A27</font></i></a>, <a class="ref" href="bagorder.html#D9" target="_self" title="BAGORDER:def.9">Def9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E28:51_1"/>
<span class="p1">(<span class="default"><a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c13">a</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">Y</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="E9:51"/><b>then </b>
 <a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font> <a href="wellord1.html#R1" title="WELLORD1:pred.1">is_well_founded_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span>
 
<b>by </b><i><a class="ref" href="wellord1.html#D3" title="WELLORD1:def.3">WELLORD1:def 3</a></i>;<br/>
<a NAME="E10:51"/><b>then </b>
 <a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font> <a href="wellord1.html#R2" title="WELLORD1:pred.2">well_orders</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bagorder.html#E2:51"><i><font color="Green" title="E31">A2</font></i></a>, <a class="txt" href="bagorder.html#E3:51"><i><font color="Green" title="E32">A3</font></i></a>, <a class="txt" href="bagorder.html#E4:51"><i><font color="Green" title="E33">A4</font></i></a>, <a class="txt" href="bagorder.html#E5:51"><i><font color="Green" title="E34">A5</font></i></a>, <a class="txt" href="bagorder.html#E6:51"><i><font color="Green" title="E35">A6</font></i></a>, <a class="ref" href="wellord1.html#D5" title="WELLORD1:def.5">WELLORD1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E11:51"/>
 <a href="bagorder.html#K7" title="BAGORDER:func.7">GrInvLexOrder</a> <font color="Maroon" title="c1">o</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>
 <b>by </b><i><a class="ref" href="wellord1.html#T8" title="WELLORD1:th.8">WELLORD1:8</a></i>;<br/>


</div>
