<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</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  non <a href="xboole_0.html#V1">empty</a> <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">G</font> be   <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">p</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">q</font> be  <a href="polynom7.html#V1">non-zero</a> <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/>













<b>assume </b><a NAME="E1:58"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp;  <a href="termord.html#K3">HT</a> <font color="Maroon">q</font>,<font color="Maroon">T</font> <a href="polynom1.html#R3">divides</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> )
 ;<br/>

<b>assume </b><a NAME="E2:58"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">G</font> <a href="groeb_1.html#R2" target="_self">is_Groebner_basis_of</a> <font color="Maroon">I</font>,<font color="Maroon">T</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">GG</font> = <font color="Maroon">G</font> as  non <a href="xboole_0.html#V1">empty</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> <b>by </b><i><a class="txt" href="groeb_1.html#E2:58"><i><font color="Green">E42</font></i></a></i>;<br/>
<a NAME="E4:58"/>
<font color="Maroon">GG</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">GG</font> <a href="ideal_1.html#K7">-Ideal</a> 
 
<b>by </b><i><a class="ref" href="ideal_1.html#D15">IDEAL_1:def 15</a></i>;<br/>
<a NAME="E5:58"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">G</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="txt" href="groeb_1.html#E5:58"><i><font color="Green">E43</font></i></a>, </i>;<br/>
<a NAME="E6:58"/>
for <font color="Olive">f</font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>  st <font color="Olive">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> holds <br/> <a href="polyred.html#K3">PolyRedRel</a> <font color="Maroon">G</font>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <font color="Olive">f</font>, <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>
 
<b>by </b><i><a class="txt" href="groeb_1.html#E2:58"><i><font color="Green">E42</font></i></a>, <a class="txt" href="groeb_1.html#E5:58"><i><font color="Green">E43</font></i></a>, </i>;<br/>
<a NAME="E7:58"/><b>then </b>
for <font color="Olive">f</font> being <a href="polynom7.html#V1">non-zero</a> <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>  st <font color="Olive">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> holds <br/><font color="Olive">f</font> <a href="polyred.html#R7">is_reducible_wrt</a> <font color="Maroon">G</font>,<font color="Maroon">T</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:58"/><b>then </b><i><font color="Green">E44</font></i>: 
for <font color="Olive">f</font> being <a href="polynom7.html#V1">non-zero</a> <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>  st <font color="Olive">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> holds <br/><font color="Olive">f</font> <a href="polyred.html#R10">is_top_reducible_wrt</a> <font color="Maroon">G</font>,<font color="Maroon">T</font>
 
<b>by </b><i><a class="txt" href="groeb_1.html#E8:58"><i><font color="Green">E44</font></i></a>, </i>;<br/>
<b>set </b><font color="Maroon">G'</font> = <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span>;<br/>
<a NAME="E9:58"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">q</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>
 
<b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/>
<a NAME="E10:58"/>
<font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E11:58"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="txt" href="groeb_1.html#E8:58"><i><font color="Green">E44</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E12:58"/><i><font color="Green">E47</font></i>: 
not <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span>
 
<b>by </b><i><a class="txt" href="groeb_1.html#E2:58"><i><font color="Green">E42</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E13:58"/><b>then </b>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span>
 
<b>by </b><i><a class="txt" href="groeb_1.html#E2:58"><i><font color="Green">E42</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E14:58"/><b>then </b>
 <a href="termord.html#K3">HT</a> <font color="Maroon">q</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Olive">u</font>,<font color="Maroon">T</font></span>)</span> where <font color="Olive">u</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> : ( <font color="Olive">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span> &amp; <font color="Olive">u</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>}</span> 
 
<b>by </b><i><a class="txt" href="groeb_1.html#E11:58"><i><font color="Green">E46</font></i></a></i>;<br/>
<a NAME="E15:58"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">q</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a>  <a href="groeb_1.html#K2" target="_self">HT</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span></span>)</span>,<font color="Maroon">T</font>
 
;<br/>
<a NAME="E16:58"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></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#E2:58"><i><font color="Green">E42</font></i></a>, <a class="txt" href="groeb_1.html#E15:58"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E17:58"/>
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="groeb_1.html#K2" target="_self">HT</a> <font color="Maroon">I</font>,<font color="Maroon">T</font> holds <br/> ex <font color="Olive">b'</font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> st <br/>( <font color="Olive">b'</font> <a href="hidden.html#R2">in</a>  <a href="groeb_1.html#K2" target="_self">HT</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span></span>)</span>,<font color="Maroon">T</font> &amp; <font color="Olive">b'</font> <a href="polynom1.html#R3">divides</a> <font color="Olive">b</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">b</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>;<br/>

<b>assume </b><a NAME="E1:58_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="groeb_1.html#K2" target="_self">HT</a> <font color="Maroon">I</font>,<font color="Maroon">T</font>
 ;<br/>

<b>then consider </b><font color="Maroon">bb</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E3:58_1"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">bb</font> <a href="hidden.html#R2">in</a>  <a href="groeb_1.html#K2" target="_self">HT</a> <font color="Maroon">G</font>,<font color="Maroon">T</font> &amp; <font color="Maroon">bb</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="txt" href="groeb_1.html#E9:58"><i><font color="Green">E45</font></i></a>, </i>;<br/>
<a NAME="E4:58_1"/>
<font color="Maroon">bb</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Olive">r</font>,<font color="Maroon">T</font></span>)</span> where <font color="Olive">r</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> : ( <font color="Olive">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> &amp; <font color="Olive">r</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>}</span> 
 
<b>by </b><i><a class="txt" href="groeb_1.html#E3"><i><font color="Green">Lemma51</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">r</font> being   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font><b> such that </b><br/><a NAME="E6:58_1"/><i><font color="Green">E73</font></i>: 
( <font color="Maroon">bb</font> <a href="pboole.html#R6">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">r</font>,<font color="Maroon">T</font> &amp; <font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> &amp; <font color="Maroon">r</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><a class="txt" onclick="hs2(this)" href="javascript:()" title="58_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:58_1_1_1"/>
( <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> or <font color="Maroon">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_1"><b>case </b></a><a NAME="E1:58_1_1_1_1"/>
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 ;<br/><div class="add"><a NAME="E2:58_1_1_1_1"/><b>then </b>
 <a href="termord.html#K3">HT</a> <font color="Maroon">q</font>,<font color="Maroon">T</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E2:58"><i><font color="Green">E42</font></i></a>, <a class="txt" href="groeb_1.html#E3"><i><font color="Green">Lemma51</font></i></a>, , </i>;<br/><b>hence </b><a NAME="E3:58_1_1_1_1"/>
 ex <font color="Olive">b'</font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> st <br/>( <font color="Olive">b'</font> <a href="hidden.html#R2">in</a>  <a href="groeb_1.html#K2" target="_self">HT</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span></span>)</span>,<font color="Maroon">T</font> &amp; <font color="Olive">b'</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="txt" href="groeb_1.html#E16:58"><i><font color="Green">E49</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_2"><b>case </b></a><a NAME="E1:58_1_1_1_2"/>
<font color="Maroon">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font>
 ;<br/><div class="add"><a NAME="E2:58_1_1_1_2"/><b>then </b>
not <font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:58_1_1_1_2"/><b>then </b>
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E4:58_1_1_1_2"/><b>then </b>
<font color="Maroon">bb</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Olive">u</font>,<font color="Maroon">T</font></span>)</span> where <font color="Olive">u</font> is   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> : ( <font color="Olive">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span> &amp; <font color="Olive">u</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>}</span> 
 <b>by </b><i/>;<br/><a NAME="E5:58_1_1_1_2"/><b>then </b>
<font color="Maroon">bb</font> <a href="hidden.html#R2">in</a>  <a href="groeb_1.html#K2" target="_self">HT</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span></span>)</span>,<font color="Maroon">T</font>
 ;<br/><b>hence </b><a NAME="E6:58_1_1_1_2"/>
 ex <font color="Olive">b'</font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> st <br/>( <font color="Olive">b'</font> <a href="hidden.html#R2">in</a>  <a href="groeb_1.html#K2" target="_self">HT</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span></span>)</span>,<font color="Maroon">T</font> &amp; <font color="Olive">b'</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="txt" href="groeb_1.html#E3"><i><font color="Green">Lemma51</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:58_1"/>
 ex <font color="Olive">b'</font> being  <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> st <br/>( <font color="Olive">b'</font> <a href="hidden.html#R2">in</a>  <a href="groeb_1.html#K2" target="_self">HT</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span></span>)</span>,<font color="Maroon">T</font> &amp; <font color="Olive">b'</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b</font> )
 ;<br/>


</div><b>end;</b></div>
<a NAME="E18:58"/><b>then </b>
 <a href="groeb_1.html#K2" target="_self">HT</a> <font color="Maroon">I</font>,<font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="groeb_1.html#K3" target="_self">multiples</a> <span class="p1">(<span class="default"><a href="groeb_1.html#K2" target="_self">HT</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span></span>)</span>,<font color="Maroon">T</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E19:58"/>
<font color="Maroon">G</font> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="groeb_1.html#K1" target="_self">{</a><span class="default"><font color="Maroon">p</font></span><a href="groeb_1.html#K1" target="_self">}</a></span> <a href="groeb_1.html#R2" target="_self">is_Groebner_basis_of</a> <font color="Maroon">I</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="txt" href="groeb_1.html#E12:58"><i><font color="Green">E47</font></i></a>, , </i>;<br/>


</div>
