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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a> <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a> <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a> <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a> <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a> <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a> <a href="algstr_1.html#V1" title="ALGSTR_1:attr.1">left_zeroed</a>  <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c4">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K29" title="POLYNOM1:func.29">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c5">f'</font>, <font color="Maroon" title="c6">h'</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/>









<b>assume </b><a NAME="E1:80"/><i><font color="Green" title="E61">A1</font></i>: 
<font color="Maroon" title="c5">f'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="80_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:80_1"/>
( <font color="Maroon" title="c6">h'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or <font color="Maroon" title="c6">h'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">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="80_1_1"><b>suppose </b></a><a NAME="E1:80_1_1"/>
<font color="Maroon" title="c6">h'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ;<br/><div class="add"><a NAME="E2:80_1_1"/><b>then </b>
<font color="Maroon" title="c6">h'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="polyred.html#T5" target="_self" title="POLYRED:th.5">Th5</a></i>;<br/><b>hence </b><a NAME="E3:80_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c6">h'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#T13" title="REWRITE1:th.13">REWRITE1:13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="80_1_2"><b>suppose </b></a><a NAME="E1:80_1_2"/>
<font color="Maroon" title="c6">h'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">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="c7">h</font> = <font color="Maroon" title="c6">h'</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="c8">H</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">g</font> where <font color="Olive" title="b1">g</font> is   <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> : not  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b1">g</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> </span>}</span> ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="80_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:80_1_2_1_1"/>
( <font color="Maroon" title="c5">f'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or <font color="Maroon" title="c5">f'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">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="80_1_2_1_1_1"><b>case </b></a><a NAME="E1:80_1_2_1_1_1"/>
<font color="Maroon" title="c5">f'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ;<br/><div class="add"><a NAME="E2:80_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c6">h'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T87" title="POLYNOM1:th.87">POLYNOM1:87</a></i>;<br/><b>hence </b><a NAME="E3:80_1_2_1_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c6">h'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#T13" title="REWRITE1:th.13">REWRITE1:13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="80_1_2_1_1_2"><b>case </b></a><a NAME="E1:80_1_2_1_1_2"/>
<font color="Maroon" title="c5">f'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">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="c9">f</font> = <font color="Maroon" title="c5">f'</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>assume </b><a NAME="E3:80_1_2_1_1_2"/>
not  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c6">h'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ;<br/><a NAME="E4:80_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E62">A2</font></i>: 
<font color="Maroon" title="c7">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">g</font> where <font color="Olive" title="b1">g</font> is   <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> : not  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b1">g</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> </span>}</span> 
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1_2_1_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:80_1_2_1_1_2_1"/>
<font color="Maroon" title="c10">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">g</font> where <font color="Olive" title="b1">g</font> is   <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> : not  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b1">g</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c11">g'</font> being   <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> such that </b><br/><a NAME="E3:80_1_2_1_1_2_1"/><i><font color="Green" title="E63">A3</font></i>: 
( <font color="Maroon" title="c10">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">g'</font> &amp; not  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c11">g'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 ;<br/><b>thus </b><a NAME="E4:80_1_2_1_1_2_1"/>
<font color="Maroon" title="c10">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K29" title="POLYNOM1:func.29">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E3:80_1_2_1_1_2_1"><i><font color="Green" title="E63">A3</font></i></a>, <a class="ref" href="polynom1.html#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></i>;<br/></div><b>end;</b></div><b>then reconsider </b><font color="Maroon" title="c10">H</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">g</font> where <font color="Olive" title="b1">g</font> is   <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> : not  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b1">g</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> </span>}</span>  as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K29" title="POLYNOM1:func.29">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> <b>by </b><i><a class="txt" href="polyred.html#E4:80_1_2_1_1_2"><i><font color="Green" title="E62">A2</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1_2_1_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:80_1_2_1_1_2_2"/>
<font color="Maroon" title="c10">H</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><b>reconsider </b><font color="Maroon" title="c11">H</font> = <font color="Maroon" title="c10">H</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="c12">m</font> being   <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> such that </b><br/><a NAME="E4:80_1_2_1_1_2_2"/><i><font color="Green" title="E63">A4</font></i>: 
( <font color="Maroon" title="c12">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">H</font> &amp; ( for <font color="Olive" title="b1">m'</font> being  <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>  st <font color="Olive" title="b1">m'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">H</font> holds <br/><font color="Maroon" title="c12">m</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Olive" title="b1">m'</font>,<font color="Maroon" title="c2">T</font> ) )
 <b>by </b><i><a class="ref" href="polyred.html#T31" target="_self" title="POLYRED:th.31">Th31</a></i>;<br/><a NAME="E5:80_1_2_1_1_2_2"/>
<font color="Maroon" title="c12">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1_2_1_1_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:80_1_2_1_1_2_2_1"/><i><font color="Green" title="E64">A5</font></i>: 
<font color="Maroon" title="c12">m</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c13">g'</font> being   <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> such that </b><br/><a NAME="E3:80_1_2_1_1_2_2_1"/><i><font color="Green" title="E65">A6</font></i>: 
( <font color="Maroon" title="c12">m</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c13">g'</font> &amp; not  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c13">g'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E4:80_1_2_1_1_2_2"><i><font color="Green" title="E63">A4</font></i></a></i>;<br/>
<a NAME="E4:80_1_2_1_1_2_2_1"/>
<font color="Maroon" title="c12">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E1:80_1_2_1_1_2_2_1"><i><font color="Green" title="E64">A5</font></i></a>, <a class="ref" href="polyred.html#T5" target="_self" title="POLYRED:th.5">Th5</a></i>;<br/>
<b>hence </b><a NAME="E5:80_1_2_1_1_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="polyred.html#E3:80_1_2_1_1_2_2_1"><i><font color="Green" title="E65">A6</font></i></a>, <a class="ref" href="rewrite1.html#T13" title="REWRITE1:th.13">REWRITE1:13</a></i>;<br/>


</div><b>end;</b></div><b>then reconsider </b><font color="Maroon" title="c13">m</font> = <font color="Maroon" title="c12">m</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/><a NAME="E7:80_1_2_1_1_2_2"/><i><font color="Green" title="E64">A7</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="termord.html#T31" title="TERMORD:th.31">TERMORD:31</a></i>;<br/><a NAME="E8:80_1_2_1_1_2_2"/>
<font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">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="E9:80_1_2_1_1_2_2"/><b>then </b>
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</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> 
 <b>by </b><i><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></i>;<br/><a NAME="E10:80_1_2_1_1_2_2"/><b>then </b><i><font color="Green" title="E65">A8</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K11" title="POLYNOM1:func.11">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><b>set </b><font color="Maroon" title="c14">g</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p5">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c9">f</font></span>)</span></span>)</span>;<br/><a NAME="E11:80_1_2_1_1_2_2"/>
( <font color="Maroon" title="c9">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">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="E12:80_1_2_1_1_2_2"/><b>then </b><i><font color="Green" title="E66">A9</font></i>: 
<font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p5">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c9">f</font></span>)</span></span>)</span>,<font color="Maroon" title="c9">f</font>, <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E7:80_1_2_1_1_2_2"><i><font color="Green" title="E64">A7</font></i></a>, <a class="txt" href="polyred.html#E10:80_1_2_1_1_2_2"><i><font color="Green" title="E65">A8</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self" title="POLYRED:def.5">Def5</a></i>;<br/><a NAME="E13:80_1_2_1_1_2_2"/>
<font color="Maroon" title="c9">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K25" title="POLYNOM1:func.25">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="E14:80_1_2_1_1_2_2"/><b>then </b><i><font color="Green" title="E67">A10</font></i>: 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></i>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c9">f</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p3">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T32" title="TERMORD:th.32">TERMORD:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D23" title="VECTSP_1:def.23">VECTSP_1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c3">L</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>
<b>by </b><i><a class="txt" href="polyred.html#E14:80_1_2_1_1_2_2"><i><font color="Green" title="E67">A10</font></i></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13" title="VECTSP_1:def.13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="ref" href="polyred.html#T22" target="_self" title="POLYRED:th.22">Th22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="ref" href="termord.html#D8" title="TERMORD:def.8">TERMORD:def 8</a></i>
;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="polynom1.html#K14" title="POLYNOM1:func.14">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p5">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c9">f</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="polynom1.html#K22" title="POLYNOM1:func.22">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K23" title="POLYNOM1:func.23">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">f</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c13">m</font></span>)</span> <a href="polynom1.html#K22" title="POLYNOM1:func.22">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <span class="p2">(<span class="default"><a href="polynom1.html#K23" title="POLYNOM1:func.23">-</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T6" target="_self" title="POLYRED:th.6">Th6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K22" title="POLYNOM1:func.22">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K23" title="POLYNOM1:func.23">-</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="ref" href="polynom1.html#T85" title="POLYNOM1:th.85">POLYNOM1:85</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>
<b>by </b><i><a class="ref" href="termord.html#D9" title="TERMORD:def.9">TERMORD:def 9</a></i>
;<br/><a NAME="E17:80_1_2_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E12:80_1_2_1_1_2_2"><i><font color="Green" title="E66">A9</font></i></a>, <a class="ref" href="polyred.html#D6" target="_self" title="POLYRED:def.6">Def6</a></i>;<br/><a NAME="E18:80_1_2_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:80"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="polyred.html#D7" target="_self" title="POLYRED:def.7">Def7</a></i>;<br/><a NAME="E19:80_1_2_1_1_2_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"><font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</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="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D13" target="_self" title="POLYRED:def.13">Def13</a></i>;<br/><a NAME="E20:80_1_2_1_1_2_2"/><b>then </b><i><font color="Green" title="E68">A11</font></i>: 
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c13">m</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>,<span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#T16" title="REWRITE1:th.16">REWRITE1:16</a></i>;<br/><a NAME="E21:80_1_2_1_1_2_2"/>
 <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#T35" target="_self" title="POLYRED:th.35">Th35</a></i>;<br/><a NAME="E22:80_1_2_1_1_2_2"/><b>then </b>
not <font color="Maroon" title="c13">m</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#T29" target="_self" title="POLYRED:th.29">Th29</a></i>;<br/><a NAME="E23:80_1_2_1_1_2_2"/><b>then </b>
not  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">H</font>
 <b>by </b><i><a class="txt" href="polyred.html#E4:80_1_2_1_1_2_2"><i><font color="Green" title="E63">A4</font></i></a></i>;<br/><a NAME="E24:80_1_2_1_1_2_2"/><b>then </b><i><font color="Green" title="E69">A12</font></i>: 
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c13">m</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ;<br/><b>consider </b><font color="Maroon" title="c15">u</font> being   <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> such that </b><br/><a NAME="E26:80_1_2_1_1_2_2"/><i><font color="Green" title="E70">A13</font></i>: 
( <font color="Maroon" title="c13">m</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c15">u</font> &amp; not  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c15">u</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c9">f</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E4:80_1_2_1_1_2_2"><i><font color="Green" title="E63">A4</font></i></a></i>;<br/><b>thus </b><a NAME="E27:80_1_2_1_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="polyred.html#E20:80_1_2_1_1_2_2"><i><font color="Green" title="E68">A11</font></i></a>, <a class="txt" href="polyred.html#E24:80_1_2_1_1_2_2"><i><font color="Green" title="E69">A12</font></i></a>, <a class="txt" href="polyred.html#E26:80_1_2_1_1_2_2"><i><font color="Green" title="E70">A13</font></i></a>, <a class="ref" href="rewrite1.html#T17" title="REWRITE1:th.17">REWRITE1:17</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:80_1_2_1_1_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c6">h'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:80_1_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c6">h'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c5">f'</font>, <a href="polynom1.html#K25" title="POLYNOM1:func.25">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
