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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/><b>let </b><font color="Maroon" title="c2">T</font> be  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a> <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>;<br/><b>let </b><font color="Maroon" title="c3">L</font> be  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> non <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a>  <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">LoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c4">p'</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/>







<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:56_1"/>
( <font color="Maroon" title="c4">p'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or <font color="Maroon" title="c4">p'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_1"><b>suppose </b></a><a NAME="E1:56_1_1"/><i><font color="Green" title="E47">A1</font></i>: 
<font color="Maroon" title="c4">p'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:56_1_1_1"/>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font></span>)</span> <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="c5">u</font> being   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E3:56_1_1_1"/><i><font color="Green" title="E48">A2</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">u</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="polynom7.html#T6" title="POLYNOM7:th.6">POLYNOM7:6</a></i>;<br/><a NAME="E4:56_1_1_1"/><i><font color="Green" title="E49">A3</font></i>: 
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E3:56_1_1_1"><i><font color="Green" title="E48">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">v</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>;<br/><b>assume </b><a NAME="E1:56_1_1_1_1"/>
<font color="Maroon" title="c6">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 ;<br/><a NAME="E2:56_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v</font>
 <b>by </b><i><a class="txt" href="polyred.html#E3:56_1_1_1"><i><font color="Green" title="E48">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:56_1_1_1_1"/>
<font color="Maroon" title="c6">v</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c5">u</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T6" title="TERMORD:th.6">TERMORD:6</a></i>;<br/></div><b>end;</b></div><a NAME="E6:56_1_1_1"/><b>then </b><i><font color="Green" title="E50">A4</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u</font>
 <b>by </b><i><a class="txt" href="polyred.html#E4:56_1_1_1"><i><font color="Green" title="E49">A3</font></i></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c3">L</font> = 
<font color="Maroon" title="c4">p'</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="txt" href="polyred.html#E1:56_1_1"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="polynom1.html#T81" title="POLYNOM1:th.81">POLYNOM1:81</a></i>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font>
<b>by </b><i><a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></i>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font>
<b>by </b><i><a class="ref" href="termord.html#T27" title="TERMORD:th.27">TERMORD:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c5">u</font>
<b>by </b><i><a class="txt" href="polyred.html#E6:56_1_1_1"><i><font color="Green" title="E50">A4</font></i></a>, <a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></i>
;<br/><b>hence </b><a NAME="E8:56_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="polyred.html#E4:56_1_1_1"><i><font color="Green" title="E49">A3</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div><a NAME="E3:56_1_1"/><b>then </b>
 <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></i>;<br/><b>hence </b><a NAME="E4:56_1_1"/>
 <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:56_1_1"><i><font color="Green" title="E47">A1</font></i></a>, <a class="ref" href="polyred.html#T25" target="_self" title="POLYRED:th.25">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_1_2"><b>suppose </b></a><a NAME="E1:56_1_2"/>
<font color="Maroon" title="c4">p'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c5">p</font> = <font color="Maroon" title="c4">p'</font> as  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <b>by </b><i><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></i>;<br/><b>set </b><font color="Maroon" title="c6">hmp</font> =  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font>;<br/><b>set </b><font color="Maroon" title="c7">R</font> =  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #);<br/><b>set </b><font color="Maroon" title="c8">x</font> =  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font>;<br/><b>set </b><font color="Maroon" title="c9">y</font> =  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font>;<br/><i><font color="Green" title="E47">A5</font></i>:  <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> = 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font>
<b>by </b><i><a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></i>
<br/>.= 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font>
<b>by </b><i><a class="ref" href="termord.html#T26" title="TERMORD:th.26">TERMORD:26</a></i>
;<br/><a NAME="E4:56_1_2"/><b>then </b><i><font color="Green" title="E48">A6</font></i>: 
 <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></i>;<br/><a NAME="E5:56_1_2"/><i><font color="Green" title="E49">A7</font></i>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></i>;<br/><a NAME="E6:56_1_2"/><b>then </b>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c5">p</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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></i>;<br/><a NAME="E7:56_1_2"/><b>then </b><i><font color="Green" title="E50">A8</font></i>: 
 <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</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/><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<font color="Maroon" title="c5">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T18" title="TERMORD:th.18">TERMORD:18</a></i>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font>
<b>by </b><i><a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></i>
;<br/><a NAME="E9:56_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="txt" href="polyred.html#E5:56_1_2"><i><font color="Green" title="E49">A7</font></i></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></i>;<br/><a NAME="E10:56_1_2"/><b>then </b><i><font color="Green" title="E51">A9</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E11:56_1_2"/><b>then </b><i><font color="Green" title="E52">A10</font></i>: 
 <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</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/><a NAME="E12:56_1_2"/><i><font color="Green" title="E53">A11</font></i>: 
( <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #) &amp; <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #) )
 <b>by </b><i><a class="ref" href="bagorder.html#T38" title="BAGORDER:th.38">BAGORDER:38</a></i>;<br/><a NAME="E13:56_1_2"/>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="polyred.html#E10:56_1_2"><i><font color="Green" title="E51">A9</font></i></a>, <a class="ref" href="termord.html#T21" title="TERMORD:th.21">TERMORD:21</a></i>;<br/><a NAME="E14:56_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></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="polyred.html#E3:56_1_2"><i><font color="Green" title="E47">A5</font></i></a>, <a class="ref" href="xboole_1.html#T37" title="XBOOLE_1:th.37">XBOOLE_1:37</a></i>;<br/><a NAME="E15:56_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p5">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p0">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p5">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></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="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="bagorder.html#K12" title="BAGORDER:func.12">FinOrd-Approx</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E12:56_1_2"><i><font color="Green" title="E53">A11</font></i></a>, <a class="ref" href="bagorder.html#T36" title="BAGORDER:th.36">BAGORDER:36</a></i>;<br/><a NAME="E16:56_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</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="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="bagorder.html#K12" title="BAGORDER:func.12">FinOrd-Approx</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E4:56_1_2"><i><font color="Green" title="E48">A6</font></i></a>, <a class="txt" href="polyred.html#E7:56_1_2"><i><font color="Green" title="E50">A8</font></i></a>, <a class="txt" href="polyred.html#E11:56_1_2"><i><font color="Green" title="E52">A10</font></i></a>, <a class="ref" href="bagorder.html#T36" title="BAGORDER:th.36">BAGORDER:36</a></i>;<br/><a NAME="E17:56_1_2"/><b>then </b><i><font color="Green" title="E54">A12</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</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#K13" title="BAGORDER:func.13">FinOrd</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <b>by </b><i><a class="ref" href="bagorder.html#D17" title="BAGORDER:def.17">BAGORDER:def 17</a></i>;<br/><b>thus </b><a NAME="E18:56_1_2"/>
 <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c4">p'</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E17:56_1_2"><i><font color="Green" title="E54">A12</font></i></a>, <a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
