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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#V2" title="BAGORDER:attr.2">admissible</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  non <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a>  <a href="struct_0.html#L2" title="STRUCT_0:struct.2">ZeroStr</a> ;<br/><b>let </b><font color="Maroon" title="c4">p</font> be  <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>;<br/><b>let </b><font color="Maroon" title="c5">b</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>;<br/>









<b>set </b><font color="Maroon" title="c6">htp</font> =  <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>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:28_1"/>
(  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</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>  or  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</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>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_1"><b>suppose </b></a><a NAME="E1:28_1_1"/><i><font color="Green" title="E25">A1</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</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> 
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_1_1"/>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">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> 
 ;<br/><b>then reconsider </b><font color="Maroon" title="c7">sp</font> =  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/><b>consider </b><font color="Maroon" title="c8">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c7">sp</font>;<br/><a NAME="E4:28_1_1_1"/>
<font color="Maroon" title="c8">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c9">u'</font> = <font color="Maroon" title="c8">u</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">n</font> ;<br/><a NAME="E6:28_1_1_1"/>
<font color="Maroon" title="c5">b</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c9">u'</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T54" title="POLYNOM1:th.54">POLYNOM1:54</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c9">u'</font></span>)</span> = 
<font color="Maroon" title="c4">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c9">u'</font></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">-'</a> <font color="Maroon" title="c5">b</font></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#D1" target="_self" title="POLYRED:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c4">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c9">u'</font>
<b>by </b><i><a class="ref" href="polynom1.html#T52" title="POLYNOM1:th.52">POLYNOM1:52</a></i>
;<br/><a NAME="E8:28_1_1_1"/><b>then </b><i><font color="Green" title="E26">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c9">u'</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="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E9:28_1_1_1"/>
<font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c9">u'</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">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/><b>hence </b><a NAME="E10:28_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="polyred.html#E1:28_1_1"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="polyred.html#E8:28_1_1_1"><i><font color="Green" title="E26">A2</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="E3:28_1_1"/><b>then </b>
<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>
 <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="E4:28_1_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</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">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</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="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_2"><b>suppose </b></a><a NAME="E1:28_1_2"/><i><font color="Green" title="E25">A3</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</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/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:28_1_2_1"/><i><font color="Green" title="E26">A4</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><b>reconsider </b><font color="Maroon" title="c7">sp</font> =  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</font></span>)</span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="txt" href="polyred.html#E1:28_1_2"><i><font color="Green" title="E25">A3</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c8">u</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c7">sp</font>;<br/><a NAME="E4:28_1_2_1"/>
<font color="Maroon" title="c8">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"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c9">u'</font> = <font color="Maroon" title="c8">u</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">n</font> ;<br/><a NAME="E6:28_1_2_1"/><i><font color="Green" title="E27">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c9">u'</font> <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="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E7:28_1_2_1"/><b>then </b>
<font color="Maroon" title="c5">b</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <font color="Maroon" title="c9">u'</font>
 <b>by </b><i><a class="ref" href="polyred.html#D1" target="_self" title="POLYRED:def.1">Def1</a></i>;<br/><a NAME="E8:28_1_2_1"/><b>then </b><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon" title="c4">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">u'</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">-'</a> <font color="Maroon" title="c5">b</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#E6:28_1_2_1"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="polyred.html#D1" target="_self" title="POLYRED:def.1">Def1</a></i>;<br/><a NAME="E9:28_1_2_1"/>
<font color="Maroon" title="c9">u'</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">-'</a> <font color="Maroon" title="c5">b</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">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/><b>hence </b><a NAME="E10:28_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="polyred.html#E1:28_1_2_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="polyred.html#E8:28_1_2_1"><i><font color="Green" title="E28">A6</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="E3:28_1_2"/><b>then </b>
 <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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p</font>
 <b>by </b><i><a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><a NAME="E4:28_1_2"/><b>then </b><i><font color="Green" title="E26">A7</font></i>: 
<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> <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="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E5:28_1_2"/><i><font color="Green" title="E27">A8</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p2">(<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></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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#E22"><i><font color="Green" title="E22">Lm9</font></i></a></i>;<br/><a NAME="E6:28_1_2"/>
<font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</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> 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">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/><a NAME="E7:28_1_2"/><b>then </b><i><font color="Green" title="E28">A9</font></i>: 
<font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</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> <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"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</font></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E4:28_1_2"><i><font color="Green" title="E26">A7</font></i></a>, <a class="txt" href="polyred.html#E5:28_1_2"><i><font color="Green" title="E27">A8</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">b'</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="E1:28_1_2_2"/>
<font color="Maroon" title="c7">b'</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"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</font></span>)</span>
 ;<br/><a NAME="E2:28_1_2_2"/><b>then </b><i><font color="Green" title="E29">A10</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c7">b'</font> <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="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E3:28_1_2_2"/><b>then </b>
<font color="Maroon" title="c5">b</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <font color="Maroon" title="c7">b'</font>
 <b>by </b><i><a class="ref" href="polyred.html#D1" target="_self" title="POLYRED:def.1">Def1</a></i>;<br/><b>then consider </b><font color="Maroon" title="c8">b3</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="E5:28_1_2_2"/><i><font color="Green" title="E30">A11</font></i>: 
<font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b'</font>
 <b>by </b><i><a class="ref" href="termord.html#T1" title="TERMORD:th.1">TERMORD:1</a></i>;<br/><a NAME="E6:28_1_2_2"/><i><font color="Green" title="E31">A12</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c7">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="polyred.html#E5:28_1_2_2"><i><font color="Green" title="E30">A11</font></i></a>, <a class="txt" href="polyred.html#E22"><i><font color="Green" title="E22">Lm9</font></i></a></i>;<br/><a NAME="E7:28_1_2_2"/>
<font color="Maroon" title="c8">b3</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">n</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D14" title="POLYNOM1:def.14">POLYNOM1:def 14</a></i>;<br/><a NAME="E8:28_1_2_2"/><b>then </b>
<font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p</font>
 <b>by </b><i><a class="txt" href="polyred.html#E2:28_1_2_2"><i><font color="Green" title="E29">A10</font></i></a>, <a class="txt" href="polyred.html#E6:28_1_2_2"><i><font color="Green" title="E31">A12</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E9:28_1_2_2"/><b>then </b>
<font color="Maroon" title="c8">b3</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <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>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><a NAME="E10:28_1_2_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">b3</font>,<span class="p2">(<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></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="termord.html#D2" title="TERMORD:def.2">TERMORD:def 2</a></i>;<br/><a NAME="E11:28_1_2_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">b'</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p3">(<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></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> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E5:28_1_2_2"><i><font color="Green" title="E30">A11</font></i></a>, <a class="ref" href="bagorder.html#D7" title="BAGORDER:def.7">BAGORDER:def 7</a></i>;<br/><b>hence </b><a NAME="E12:28_1_2_2"/>
<font color="Maroon" title="c7">b'</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c5">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</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>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="termord.html#D2" title="TERMORD:def.2">TERMORD:def 2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E9:28_1_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">b</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p</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">b</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</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#E7:28_1_2"><i><font color="Green" title="E28">A9</font></i></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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