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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="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> <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> <a href="group_1.html#V2" title="GROUP_1:attr.2">unital</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a> <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">distributive</a> <a href="vectsp_1.html#V9" title="VECTSP_1:attr.9">Field-like</a> non <a href="vectsp_1.html#V10" title="VECTSP_1:attr.10">degenerated</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c4">I</font> be  <a href="ideal_1.html#V1" title="IDEAL_1:attr.1">add-closed</a> <a href="ideal_1.html#V2" title="IDEAL_1:attr.2">left-ideal</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#K30" title="POLYNOM1:func.30">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">m</font> be   <a href="polynom7.html#NM1" title="POLYNOM7:NM.1">Monomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/><b>let </b><font color="Maroon" title="c6">f</font>, <font color="Maroon" title="c7">g</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="E1:56"/><i><font color="Green" title="E41">A1</font></i>: 
( <font color="Maroon" title="c6">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> &amp; <font color="Maroon" title="c7">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> )
 ;<br/>

<b>assume </b><a NAME="E2:56"/><i><font color="Green" title="E42">A2</font></i>: 
( ( for <font color="Olive" title="b1">p</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>  holds <br/>(  not <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> or  not <font color="Olive" title="b1">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> ) ) &amp; ( for <font color="Olive" title="b1">p</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>  holds <br/>(  not <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> or  not <font color="Olive" title="b1">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> ) ) )
 ;<br/>

<i><font color="Green" title="E43">A3</font></i>:  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> = 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T22" title="TERMORD:th.22">TERMORD:22</a></i>
<br/>.= 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font>
<b>by </b><i><a class="txt" href="groeb_1.html#E1:56"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="termord.html#T22" title="TERMORD:th.22">TERMORD:22</a></i>
;<br/>
<i><font color="Green" title="E44">A4</font></i>:  <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> = 
<font color="Maroon" title="c6">f</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="c6">f</font>,<font color="Maroon" title="c2">T</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"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c6">f</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="c6">f</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/>.= 
<font color="Maroon" title="c7">g</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="c7">g</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="txt" href="groeb_1.html#E1:56"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="groeb_1.html#E3:56"><i><font color="Green" title="E43">A3</font></i></a>, <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="c7">g</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/>
<b>reconsider </b><font color="Maroon" title="c8">I</font> = <font color="Maroon" title="c4">I</font> as   <a href="ideal_1.html#NM3" title="IDEAL_1:NM.3">LeftIdeal</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30" title="POLYNOM1:func.30">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="groeb_1.html#E1:56"><i><font color="Green" title="E41">A1</font></i></a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:56_3"/>
( <font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</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_3_1"><b>suppose </b></a><a NAME="E1:56_3_1"/>
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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>hence </b><font color="Maroon" title="c7">g</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <font color="Maroon" title="c7">g</font>
<b>by </b><i><a class="ref" href="polyred.html#T2" title="POLYRED:th.2">POLYRED:2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <font color="Maroon" title="c7">g</font>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <font color="Maroon" title="c7">g</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></i>
<br/>.= 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><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>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T3" title="POLYRED:th.3">POLYRED:3</a></i>
<br/>.= 
<font color="Maroon" title="c6">f</font>
<b>by </b><i><a class="ref" href="polynom1.html#T82" title="POLYNOM1:th.82">POLYNOM1:82</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_3_2"><b>suppose </b></a><a NAME="E1:56_3_2"/><i><font color="Green" title="E45">A5</font></i>: 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</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"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_3_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_3_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:56_3_2_1_1"/>
( <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c6">f</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> &amp; <font color="Maroon" title="c7">g</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_3_2_1_1_1"><b>case </b></a><a NAME="E1:56_3_2_1_1_1"/><i><font color="Green" title="E46">A6</font></i>: 
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><a NAME="E2:56_3_2_1_1_1"/><b>then </b>
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="groeb_1.html#E4:56"><i><font color="Green" title="E44">A4</font></i></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></i>;<br/><b>hence </b><a NAME="E3:56_3_2_1_1_1"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E1:56_3_2_1_1_1"><i><font color="Green" title="E46">A6</font></i></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_3_2_1_1_2"><b>case </b></a><a NAME="E1:56_3_2_1_1_2"/><i><font color="Green" title="E46">A7</font></i>: 
<font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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"><a NAME="E2:56_3_2_1_1_2"/><b>then </b>
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="groeb_1.html#E4:56"><i><font color="Green" title="E44">A4</font></i></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></i>;<br/><b>hence </b><a NAME="E3:56_3_2_1_1_2"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E1:56_3_2_1_1_2"><i><font color="Green" title="E46">A7</font></i></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="56_3_2_1_1_3"><b>case </b></a><a NAME="E1:56_3_2_1_1_3"/>
( <font color="Maroon" title="c6">f</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> &amp; <font color="Maroon" title="c7">g</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"><a NAME="E2:56_3_2_1_1_3"/><b>then </b>
(  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</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>  &amp;  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c7">g</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="E3:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E46">A8</font></i>: 
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</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="c6">f</font> &amp; ( for <font color="Olive" title="b1">b</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">b</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="c6">f</font> holds <br/><font color="Olive" title="b1">b</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="c6">f</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="E4:56_3_2_1_1_3"/>
( not <font color="Maroon" title="c6">f</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> &amp; not <font color="Maroon" title="c7">g</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> )
 <b>by </b><i><a class="txt" href="groeb_1.html#E1:56"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="groeb_1.html#E2:56"><i><font color="Green" title="E42">A2</font></i></a></i>;<br/><a NAME="E5:56_3_2_1_1_3"/><b>then </b>
( <font color="Maroon" title="c6">f</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> &amp; <font color="Maroon" title="c7">g</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> )
 <b>by </b><i><a class="ref" href="polyred.html#T29" title="POLYRED:th.29">POLYRED:29</a></i>;<br/><a NAME="E6:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E47">A9</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c7">g</font>
 <b>by </b><i><a class="ref" href="polyred.html#T26" title="POLYRED:th.26">POLYRED:26</a></i>;<br/><a NAME="E7:56_3_2_1_1_3"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K2" title="TERMORD:func.2">max</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</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="groeb_1.html#E3:56"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="groeb_1.html#T7" target="_self" title="GROEB_1:th.7">Th7</a></i>;<br/><a NAME="E8:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E48">A10</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</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="c6">f</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#T12" title="TERMORD:th.12">TERMORD:12</a></i>;<br/><a NAME="E9:56_3_2_1_1_3"/><i><font color="Green" title="E49">A11</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</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="txt" href="groeb_1.html#E1:56_3_2"><i><font color="Green" title="E45">A5</font></i></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></i>;<br/><a NAME="E10:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E50">A12</font></i>: 
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</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#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span> &amp; ( for <font color="Olive" title="b1">b</font> being  <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>  st <font color="Olive" title="b1">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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span> holds <br/><font color="Olive" title="b1">b</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_3_2_1_1_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:56_3_2_1_1_3_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>
 ;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c7">g</font></span>)</span></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="c6">f</font>,<font color="Maroon" title="c2">T</font></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="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="groeb_1.html#E3:56"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="polynom1.html#D21" title="POLYNOM1:def.21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22" title="POLYNOM1:def.22">POLYNOM1: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="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></i>
<br/>.= 
 <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="groeb_1.html#E4:56"><i><font color="Green" title="E44">A4</font></i></a>, <a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></i>
;<br/><b>hence </b><a NAME="E3:56_3_2_1_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_1.html#E10:56_3_2_1_1_3"><i><font color="Green" title="E50">A12</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="E12:56_3_2_1_1_3"/><b>then </b>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E8:56_3_2_1_1_3"><i><font color="Green" title="E48">A10</font></i></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></i>;<br/><a NAME="E13:56_3_2_1_1_3"/><b>then </b>
not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T5" title="TERMORD:th.5">TERMORD:5</a></i>;<br/><a NAME="E14:56_3_2_1_1_3"/><b>then </b>
not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</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"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>
 <b>by </b><i><a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><a NAME="E15:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E51">A13</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</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="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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/><b>set </b><font color="Maroon" title="c9">s</font> =  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font>;<br/><a NAME="E16:56_3_2_1_1_3"/><i><font color="Green" title="E52">A14</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c7">g</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/><a NAME="E17:56_3_2_1_1_3"/>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T79" title="POLYNOM1:th.79">POLYNOM1:79</a></i>;<br/><a NAME="E18:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E53">A15</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c7">g</font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_1.html#E16:56_3_2_1_1_3"><i><font color="Green" title="E52">A14</font></i></a>, <a class="ref" href="groeb_1.html#T5" target="_self" title="GROEB_1:th.5">Th5</a></i>;<br/><a NAME="E19:56_3_2_1_1_3"/><i><font color="Green" title="E54">A16</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</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#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_1.html#E9:56_3_2_1_1_3"><i><font color="Green" title="E49">A11</font></i></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><b>set </b><font color="Maroon" title="c10">d</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon" title="c11">c</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span>;<br/><b>set </b><font color="Maroon" title="c12">h</font> = <font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>;<br/><i><font color="Green" title="E55">A17</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c7">g</font></span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></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="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21" title="POLYNOM1:def.21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22" title="POLYNOM1:def.22">POLYNOM1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></i>
;<br/><a NAME="E21:56_3_2_1_1_3"/>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></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/><a NAME="E22:56_3_2_1_1_3"/><b>then </b>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T79" title="POLYNOM1:th.79">POLYNOM1:79</a></i>;<br/><a NAME="E23:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E56">A18</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="groeb_1.html#T5" target="_self" title="GROEB_1:th.5">Th5</a></i>;<br/><a NAME="E24:56_3_2_1_1_3"/>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>
 <b>by </b><i><a class="ref" href="polyred.html#T19" title="POLYRED:th.19">POLYRED:19</a></i>;<br/><a NAME="E25:56_3_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></i>;<br/><a NAME="E26:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E57">A19</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_1.html#E23:56_3_2_1_1_3"><i><font color="Green" title="E56">A18</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E27:56_3_2_1_1_3"/>
<span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_1.html#E6:56_3_2_1_1_3"><i><font color="Green" title="E47">A9</font></i></a>, <a class="txt" href="groeb_1.html#E18:56_3_2_1_1_3"><i><font color="Green" title="E53">A15</font></i></a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></i>;<br/><a NAME="E28:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E58">A20</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E26:56_3_2_1_1_3"><i><font color="Green" title="E57">A19</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><i><font color="Green" title="E59">A21</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></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="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span></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="c6">f</font>,<font color="Maroon" title="c2">T</font></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="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21" title="POLYNOM1:def.21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22" title="POLYNOM1:def.22">POLYNOM1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c3">L</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="groeb_1.html#E15:56_3_2_1_1_3"><i><font color="Green" title="E51">A13</font></i></a>, <a class="ref" href="polynom7.html#D10" title="POLYNOM7:def.10">POLYNOM7:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c3">L</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c3">L</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T25" title="RLVECT_1:th.25">RLVECT_1:25</a></i>
<br/>.= 
<font color="Maroon" title="c6">f</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="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>
;<br/><a NAME="E30:56_3_2_1_1_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></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="c6">f</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="groeb_1.html#E3:56_3_2_1_1_3"><i><font color="Green" title="E46">A8</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><a NAME="E31:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E60">A22</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</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"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></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="E32:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E61">A23</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>,<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="E33:56_3_2_1_1_3"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>,<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"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_1.html#E31:56_3_2_1_1_3"><i><font color="Green" title="E60">A22</font></i></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><a NAME="E34:56_3_2_1_1_3"/><b>then </b>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</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="c6">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E28:56_3_2_1_1_3"><i><font color="Green" title="E58">A20</font></i></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><a NAME="E35:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E62">A24</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E32:56_3_2_1_1_3"><i><font color="Green" title="E61">A23</font></i></a>, <a class="ref" href="termord.html#T7" title="TERMORD:th.7">TERMORD:7</a></i>;<br/><b>then </b> <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
<font color="Maroon" title="c6">f</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="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="txt" href="groeb_1.html#E29:56_3_2_1_1_3"><i><font color="Green" title="E59">A21</font></i></a>, <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> <font color="Maroon" title="c6">f</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/><b>then </b><i><font color="Green" title="E63">A25</font></i>:  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
 <a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="txt" href="groeb_1.html#E35:56_3_2_1_1_3"><i><font color="Green" title="E62">A24</font></i></a>, <a class="ref" href="termord.html#D8" title="TERMORD:def.8">TERMORD:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c5">m</font>
<b>by </b><i><a class="txt" href="groeb_1.html#E1:56"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="termord.html#D8" title="TERMORD:def.8">TERMORD:def 8</a></i>
;<br/><a NAME="E38:56_3_2_1_1_3"/><i><font color="Green" title="E64">A26</font></i>: 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E28:56_3_2_1_1_3"><i><font color="Green" title="E58">A20</font></i></a>, <a class="ref" href="groeb_1.html#T8" target="_self" title="GROEB_1:th.8">Th8</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_3_2_1_1_3_6"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:56_3_2_1_1_3_6"/><i><font color="Green" title="E65">A27</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">f</font>
 ;<br/><a NAME="E2:56_3_2_1_1_3_6"/><i><font color="Green" title="E66">A28</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="groeb_1.html#E19:56_3_2_1_1_3"><i><font color="Green" title="E54">A16</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/><i><font color="Green" title="E67">A29</font></i>:  <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span></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/>.= 
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c3">L</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="groeb_1.html#E20:56_3_2_1_1_3"><i><font color="Green" title="E55">A17</font></i></a>, <a class="txt" href="groeb_1.html#E2:56_3_2_1_1_3_6"><i><font color="Green" title="E66">A28</font></i></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></i>
<br/>.= 
 <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></i>
;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span></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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></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="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21" title="POLYNOM1:def.21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T9" title="POLYRED:th.9">POLYRED:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom7.html#D10" title="POLYNOM7:def.10">POLYNOM7:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="groeb_1.html#E20:56_3_2_1_1_3"><i><font color="Green" title="E55">A17</font></i></a>, <a class="txt" href="groeb_1.html#E3:56_3_2_1_1_3_6"><i><font color="Green" title="E67">A29</font></i></a>, <a class="ref" href="vectsp_1.html#T41" title="VECTSP_1:th.41">VECTSP_1:41</a></i>
<br/>.= 
 <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="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></i>
;<br/><b>hence </b><a NAME="E5:56_3_2_1_1_3_6"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_1.html#E6:56_3_2_1_1_3"><i><font color="Green" title="E47">A9</font></i></a>, <a class="txt" href="groeb_1.html#E10:56_3_2_1_1_3"><i><font color="Green" title="E50">A12</font></i></a>, <a class="txt" href="groeb_1.html#E18:56_3_2_1_1_3"><i><font color="Green" title="E53">A15</font></i></a>, <a class="txt" href="groeb_1.html#E1:56_3_2_1_1_3_6"><i><font color="Green" title="E65">A27</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="E40:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E65">A30</font></i>: 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E38:56_3_2_1_1_3"><i><font color="Green" title="E64">A26</font></i></a>, <a class="ref" href="polyred.html#D3" title="POLYRED:def.3">POLYRED:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">f'</font> = <font color="Maroon" title="c6">f</font>, <font color="Maroon" title="c14">g'</font> = <font color="Maroon" title="c7">g</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30" title="POLYNOM1:func.30">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="ref" href="polynom1.html#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c15">f'</font> = <font color="Maroon" title="c13">f'</font>, <font color="Maroon" title="c16">g'</font> = <font color="Maroon" title="c14">g'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30" title="POLYNOM1:func.30">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> ;<br/><b>reconsider </b><font color="Maroon" title="c17">cc</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30" title="POLYNOM1:func.30">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="ref" href="polynom1.html#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c18">cc</font> = <font color="Maroon" title="c17">cc</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30" title="POLYNOM1:func.30">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> ;<br/><a NAME="E45:56_3_2_1_1_3"/>
<font color="Maroon" title="c15">f'</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c16">g'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">I</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E1:56"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="ideal_1.html#T15" title="IDEAL_1:th.15">IDEAL_1:15</a></i>;<br/><a NAME="E46:56_3_2_1_1_3"/><b>then </b>
<font color="Maroon" title="c18">cc</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">f'</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c16">g'</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">I</font>
 <b>by </b><i><a class="ref" href="ideal_1.html#D2" title="IDEAL_1:def.2">IDEAL_1:def 2</a></i>;<br/><a NAME="E47:56_3_2_1_1_3"/><b>then </b><i><font color="Green" title="E66">A31</font></i>: 
<font color="Maroon" title="c15">f'</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">cc</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">f'</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c16">g'</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">I</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E1:56"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="ideal_1.html#T15" title="IDEAL_1:th.15">IDEAL_1:15</a></i>;<br/><a NAME="E48:56_3_2_1_1_3"/><i><font color="Green" title="E67">A32</font></i>: 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">f'</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c16">g'</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E4"><i><font color="Green" title="E3">Lm2</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c19">cp</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> <a href="polynom1.html#K29" title="POLYNOM1:func.29">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30" title="POLYNOM1:func.30">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="ref" href="polynom1.html#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c20">cp</font> = <font color="Maroon" title="c19">cp</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30" title="POLYNOM1:func.30">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> ;<br/><a NAME="E51:56_3_2_1_1_3"/><i><font color="Green" title="E68">A33</font></i>: 
<font color="Maroon" title="c20">cp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">cc</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">f'</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c16">g'</font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_1.html#E48:56_3_2_1_1_3"><i><font color="Green" title="E67">A32</font></i></a>, <a class="ref" href="polynom1.html#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></i>;<br/><font color="Maroon" title="c15">f'</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c20">cp</font> = 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</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="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</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> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> <a href="polynom1.html#K29" title="POLYNOM1:func.29">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="groeb_1.html#E4"><i><font color="Green" title="E3">Lm2</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</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="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom7.html#T27" title="POLYNOM7:th.27">POLYNOM7:27</a></i>
;<br/><b>hence </b><a NAME="E53:56_3_2_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_1.html#E2:56"><i><font color="Green" title="E42">A2</font></i></a>, <a class="txt" href="groeb_1.html#E37:56_3_2_1_1_3"><i><font color="Green" title="E63">A25</font></i></a>, <a class="txt" href="groeb_1.html#E40:56_3_2_1_1_3"><i><font color="Green" title="E65">A30</font></i></a>, <a class="txt" href="groeb_1.html#E47:56_3_2_1_1_3"><i><font color="Green" title="E66">A31</font></i></a>, <a class="txt" href="groeb_1.html#E51:56_3_2_1_1_3"><i><font color="Green" title="E68">A33</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:56_3_2"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
