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<div class="add">

<b>let </b><font color="Maroon">n</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">T</font> be  <a href="relat_2.html#V6">connected</a> <a href="bagorder.html#V2">admissible</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V2">unital</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V9">Field-like</a> non <a href="vectsp_1.html#V10">degenerated</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">I</font> be  <a href="ideal_1.html#V1">add-closed</a> <a href="ideal_1.html#V2">left-ideal</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span>;<br/><b>let </b><font color="Maroon">m</font> be   <a href="polynom7.html#NM1">Monomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Maroon">g</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/>











<b>assume </b><a NAME="E1:56"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp;  <a href="termord.html#K5">HM</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> &amp;  <a href="termord.html#K5">HM</a> <font color="Maroon">g</font>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> )
 ;<br/>

<b>assume </b><a NAME="E2:56"/><i><font color="Green">E42</font></i>: 
( ( for <font color="Olive">p</font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>  holds <br/>(  not <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> or  not <font color="Olive">p</font> <a href="polyred.html#R2">&lt;</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> or  not  <a href="termord.html#K5">HM</a> <font color="Olive">p</font>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> ) ) &amp; ( for <font color="Olive">p</font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>  holds <br/>(  not <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> or  not <font color="Olive">p</font> <a href="polyred.html#R2">&lt;</a> <font color="Maroon">g</font>,<font color="Maroon">T</font> or  not  <a href="termord.html#K5">HM</a> <font color="Olive">p</font>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> ) ) )
 ;<br/>

<i><font color="Green">E43</font></i>:  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> = 
 <a href="polynom7.html#K2">term</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T22">TERMORD:22</a></i>
<br/>.= 
 <a href="termord.html#K3">HT</a> <font color="Maroon">g</font>,<font color="Maroon">T</font>
<b>by </b><i>, <a class="ref" href="termord.html#T22">TERMORD:22</a></i>
;<br/>
<i><font color="Green">E44</font></i>:  <a href="termord.html#K4">HC</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> = 
<font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T18">TERMORD:18</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">g</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i>, <a class="txt" href="groeb_1.html#E3:56"><i><font color="Green">E43</font></i></a>, <a class="ref" href="termord.html#T18">TERMORD:18</a></i>
<br/>.= 
 <a href="termord.html#K4">HC</a> <font color="Maroon">g</font>,<font color="Maroon">T</font>
<b>by </b><i><a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>
;<br/>
<b>reconsider </b><font color="Maroon">I</font> = <font color="Maroon">I</font> as   <a href="ideal_1.html#NM3">LeftIdeal</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> <b>by </b><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">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font> or <font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">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">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>
 ;<br/><div class="add"><b>hence </b><font color="Maroon">g</font> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> <a href="polynom1.html#K23">+</a> <font color="Maroon">g</font>
<b>by </b><i><a class="ref" href="polyred.html#T2">POLYRED:2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <font color="Maroon">g</font>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">g</font></span>)</span> <a href="polynom1.html#K23">+</a> <font color="Maroon">g</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80">POLYNOM1:80</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T3">POLYRED:3</a></i>
<br/>.= 
<font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="polynom1.html#T82">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">E45</font></i>: 
<font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">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">f</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font> or <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font> or ( <font color="Maroon">f</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">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">E46</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>
 ;<br/><div class="add"><a NAME="E2:56_3_2_1_1_1"/><b>then </b>
 <a href="termord.html#K4">HC</a> <font color="Maroon">g</font>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E4:56"><i><font color="Green">E44</font></i></a>, <a class="ref" href="termord.html#T17">TERMORD:17</a></i>;<br/><b>hence </b><a NAME="E3:56_3_2_1_1_1"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E1:56_3_2_1_1_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="termord.html#T17">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">E47</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>
 ;<br/><div class="add"><a NAME="E2:56_3_2_1_1_2"/><b>then </b>
 <a href="termord.html#K4">HC</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E4:56"><i><font color="Green">E44</font></i></a>, <a class="ref" href="termord.html#T17">TERMORD:17</a></i>;<br/><b>hence </b><a NAME="E3:56_3_2_1_1_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i>, <a class="ref" href="termord.html#T17">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">f</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font> )
 ;<br/><div class="add"><a NAME="E2:56_3_2_1_1_3"/><b>then </b>
(  <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="polynom1.html#K12">Support</a> <font color="Maroon">g</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/><a NAME="E3:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E48</font></i>: 
(  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font> &amp; ( for <font color="Olive">b</font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>  st <font color="Olive">b</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font> holds <br/><font color="Olive">b</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font> ) )
 <b>by </b><i><a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E4:56_3_2_1_1_3"/>
( not <font color="Maroon">f</font> <a href="polyred.html#R2">&lt;</a> <font color="Maroon">g</font>,<font color="Maroon">T</font> &amp; not <font color="Maroon">g</font> <a href="polyred.html#R2">&lt;</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> )
 <b>by </b><i>, <a class="txt" href="groeb_1.html#E2:56"><i><font color="Green">E42</font></i></a></i>;<br/><a NAME="E5:56_3_2_1_1_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="polyred.html#R1">&lt;=</a> <font color="Maroon">g</font>,<font color="Maroon">T</font> &amp; <font color="Maroon">g</font> <a href="polyred.html#R1">&lt;=</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> )
 <b>by </b><i><a class="ref" href="polyred.html#T29">POLYRED:29</a></i>;<br/><a NAME="E6:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E49</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="polyred.html#T26">POLYRED:26</a></i>;<br/><a NAME="E7:56_3_2_1_1_3"/>
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K2">max</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E3:56"><i><font color="Green">E43</font></i></a>, </i>;<br/><a NAME="E8:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E50</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T12">TERMORD:12</a></i>;<br/><a NAME="E9:56_3_2_1_1_3"/><i><font color="Green">E73</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="groeb_1.html#E1:56_3_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/><a NAME="E10:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E74</font></i>: 
(  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> &amp; ( for <font color="Olive">b</font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>  st <font color="Olive">b</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> holds <br/><font color="Olive">b</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font>,<font color="Maroon">T</font> ) )
 <b>by </b><i><a class="ref" href="termord.html#D6">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">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font> <a href="pboole.html#R6">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>
 ;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">g</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">g</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="groeb_1.html#E3:56"><i><font color="Green">E43</font></i></a>, <a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">g</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">g</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">g</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
<b>by </b><i><a class="txt" href="groeb_1.html#E4:56"><i><font color="Green">E44</font></i></a>, <a class="ref" href="rlvect_1.html#T16">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#E8:56_3_2_1_1_3"><i><font color="Green">E50</font></i></a>, <a class="ref" href="polynom1.html#D9">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">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font> <a href="termord.html#R2">&lt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E3:56_3_2_1_1_3"><i><font color="Green">E48</font></i></a>, <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/><a NAME="E13:56_3_2_1_1_3"/><b>then </b>
not  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T5">TERMORD:5</a></i>;<br/><a NAME="E14:56_3_2_1_1_3"/><b>then </b>
not  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>
 <b>by </b><i><a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E15:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E75</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><b>set </b><font color="Maroon">s</font> =  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font>;<br/><a NAME="E16:56_3_2_1_1_3"/><i><font color="Green">E76</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>;<br/><a NAME="E17:56_3_2_1_1_3"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T79">POLYNOM1:79</a></i>;<br/><a NAME="E18:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E77</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">g</font></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E19:56_3_2_1_1_3"/><i><font color="Green">E78</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</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">E49</font></i></a>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><b>set </b><font color="Maroon">d</font> = <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">c</font> = <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span>;<br/><b>set </b><font color="Maroon">h</font> = <font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span>;<br/><i><font color="Green">E79</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">g</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D11">RLVECT_1:def 11</a></i>
;<br/><a NAME="E21:56_3_2_1_1_3"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>;<br/><a NAME="E22:56_3_2_1_1_3"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T79">POLYNOM1:79</a></i>;<br/><a NAME="E23:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E80</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E24:56_3_2_1_1_3"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>
 <b>by </b><i><a class="ref" href="polyred.html#T19">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">Support</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/><a NAME="E26:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E81</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">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">Support</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/><a NAME="E28:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E82</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E4"><i><font color="Green">Lemma57</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><i><font color="Green">E93</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</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">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="groeb_1.html#E3"><i><font color="Green">Lemma51</font></i></a>, <a class="ref" href="polynom7.html#D10">POLYNOM7:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T25">RLVECT_1:25</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7">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">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E31:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E95</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E32:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E97</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E33:56_3_2_1_1_3"/>
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_1.html#E5"><i><font color="Green">Lemma60</font></i></a>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E34:56_3_2_1_1_3"/><b>then </b>
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">T</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E35:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E98</font></i>: 
 <a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">T</font> <a href="pboole.html#R6">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="groeb_1.html#T3" target="_self">Th3</a>, <a class="ref" href="termord.html#T7">TERMORD:7</a></i>;<br/><b>then </b> <a href="termord.html#K4">HC</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">T</font> = 
<font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i>, <a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>
<br/>.= 
 <a href="termord.html#K4">HC</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>
<b>by </b><i><a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>
;<br/><b>then </b><i><font color="Green">E99</font></i>:  <a href="termord.html#K5">HM</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">T</font> = 
 <a href="polynom7.html#K1">Monom</a> <span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i>, <a class="ref" href="termord.html#D8">TERMORD:def 8</a></i>
<br/>.= 
<font color="Maroon">m</font>
<b>by </b><i>, <a class="ref" href="termord.html#D8">TERMORD:def 8</a></i>
;<br/><a NAME="E38:56_3_2_1_1_3"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="polyred.html#R1">&lt;=</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>
 <b>by </b><i>, </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">E101</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font>
 ;<br/><a NAME="E2:56_3_2_1_1_3_6"/><i><font color="Green">E102</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><i><font color="Green">E103</font></i>:  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</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">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="groeb_1.html#T6" target="_self">Th6</a>, <a class="ref" href="vectsp_1.html#D22">VECTSP_1:def 22</a></i>
<br/>.= 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>
;<br/><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</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">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polyred.html#T9">POLYRED:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom7.html#D10">POLYNOM7:def 10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="groeb_1.html#T7" target="_self">Th7</a>, <a class="ref" href="vectsp_1.html#T41">VECTSP_1:41</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">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#E8:56_3_2_1_1_3"><i><font color="Green">E50</font></i></a>, , , <a class="ref" href="polynom1.html#D9">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">E104</font></i>: 
<font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="polyred.html#R2">&lt;</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="groeb_1.html#T5" target="_self">Th5</a>, <a class="ref" href="polyred.html#D3">POLYRED:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font>, <font color="Maroon">g'</font> = <font color="Maroon">g</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/><b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f'</font>, <font color="Maroon">g'</font> = <font color="Maroon">g'</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> ;<br/><b>reconsider </b><font color="Maroon">cc</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K4">|</a> <font color="Maroon">n</font>,<font color="Maroon">L</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/><b>reconsider </b><font color="Maroon">cc</font> = <font color="Maroon">cc</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> ;<br/><a NAME="E45:56_3_2_1_1_3"/>
<font color="Maroon">f'</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">g'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i>, <a class="ref" href="ideal_1.html#T15">IDEAL_1:15</a></i>;<br/><a NAME="E46:56_3_2_1_1_3"/><b>then </b>
<font color="Maroon">cc</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">f'</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">g'</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="ideal_1.html#D2">IDEAL_1:def 2</a></i>;<br/><a NAME="E47:56_3_2_1_1_3"/><b>then </b><i><font color="Green">E106</font></i>: 
<font color="Maroon">f'</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">cc</font> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><font color="Maroon">f'</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">g'</font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i>, <a class="ref" href="ideal_1.html#T15">IDEAL_1:15</a></i>;<br/><a NAME="E48:56_3_2_1_1_3"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f'</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">g'</font>
 <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">cp</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K4">|</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/><b>reconsider </b><font color="Maroon">cp</font> = <font color="Maroon">cp</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> ;<br/><a NAME="E51:56_3_2_1_1_3"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">cp</font> <a href="hidden.html#R1">=</a> <font color="Maroon">cc</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">f'</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">g'</font></span>)</span>
 <b>by </b><i><a class="ref" href="groeb_1.html#T7" target="_self">Th7</a>, <a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/><font color="Maroon">f'</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">cp</font> = 
<font color="Maroon">f</font> <a href="polynom1.html#K25">-</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">f</font> <a href="polynom1.html#K15">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p0">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K4">|</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> <a href="polynom1.html#K29">*'</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">g</font> <a href="polynom1.html#K15">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3">HT</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span>,<font color="Maroon">T</font></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="polynom1.html#K25">-</a> <font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom7.html#T27">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">E42</font></i></a>, <a class="ref" href="groeb_1.html#T4" target="_self">Th4</a>, , <a class="ref" href="groeb_1.html#T6" target="_self">Th6</a>, <a class="ref" href="groeb_1.html#T8" target="_self">Th8</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">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
