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<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">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">P</font> be  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>;<br/><b>let </b><font color="Maroon">f</font> be   <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>, <font color="Maroon">p</font> be   <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>, <font color="Maroon">h</font> be   <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>assume </b><a NAME="E1:95"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">p</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">h</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/>

<b>set </b><font color="Maroon">PR</font> =  <a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/>
<b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font>, <font color="Maroon">h'</font> = <font color="Maroon">h</font>, <font color="Maroon">p'</font> = <font color="Maroon">p</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">f'</font> = <font color="Maroon">f'</font>, <font color="Maroon">p'</font> = <font color="Maroon">p'</font>, <font color="Maroon">h'</font> = <font color="Maroon">h'</font> as   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font> <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/>
<b>reconsider </b><font color="Maroon">h'</font> = <font color="Maroon">h'</font>, <font color="Maroon">p'</font> = <font color="Maroon">p'</font> as  <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> <b>by </b><i><a class="txt" href="polyred.html#E6"><i><font color="Green">Lemma72</font></i></a>, <a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/>
<a NAME="E5:95"/><i><font color="Green">E24</font></i>: 
 <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</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="polyred.html#E6"><i><font color="Green">Lemma72</font></i></a>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:95_1_1"/>
( <font color="Maroon">f'</font> <a href="funct_2.html#R2">=</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> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_1_1"><b>case </b></a><a NAME="E1:95_1_1_1"/>
<font color="Maroon">f'</font> <a href="funct_2.html#R2">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>
 ;<br/><div class="add"><a NAME="E2:95_1_1_1"/><b>then </b>
 <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">f'</font> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span>,<font color="Maroon">f'</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:95_1_1_1"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">f'</font>,<font color="Maroon">f'</font> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span> <a href="rewrite1.html#R2">are_convertible_wrt</a>  <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#T26">REWRITE1:26</a></i>;<br/><a NAME="E4:95_1_1_1"/>
<font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/><b>hence </b><a NAME="E5:95_1_1_1"/>
<font color="Maroon">f</font>,<font color="Maroon">f</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font></span>)</span> <a href="rewrite1.html#R2">are_convertible_wrt</a>  <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_1_2"><b>case </b></a><a NAME="E1:95_1_1_2"/>
<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>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f'</font> as  <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> <b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 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"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <font color="Maroon">f'</font> = 
<span class="p1">(<span class="default"><font color="Maroon">f'</font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">f'</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">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span> <a href="polynom1.html#K23">+</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">f'</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80">POLYNOM1:80</a></i>
<br/>.= 
<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> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font>
<b>by </b><i/>
;<br/><a NAME="E4:95_1_1_2"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <span class="p1">(<span class="default"><font color="Maroon">f'</font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <font color="Maroon">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="polyred.html#E6"><i><font color="Green">Lemma72</font></i></a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1_1_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:95_1_1_2_2_1"/>
( <font color="Maroon">f'</font> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span> <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> or <font color="Maroon">f'</font> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span> <a href="funct_2.html#R2">=</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="95_1_1_2_2_1_1"><b>case </b></a><a NAME="E1:95_1_1_2_2_1_1"/>
<font color="Maroon">f'</font> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span> <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"><b>then reconsider </b><font color="Maroon">g'</font> = <font color="Maroon">f'</font> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span> as  <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> <b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/><a NAME="E3:95_1_1_2_2_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">g'</font>,<font color="Maroon">f'</font> <a href="rewrite1.html#R2">are_convertible_wrt</a>  <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font>
 <b>by </b><i>, </i>;<br/><a NAME="E4:95_1_1_2_2_1_1"/>
<font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/><a NAME="E5:95_1_1_2_2_1_1"/><b>then </b>
<font color="Maroon">g'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/><b>hence </b><a NAME="E6:95_1_1_2_2_1_1"/>
<font color="Maroon">f</font>,<font color="Maroon">f</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font></span>)</span> <a href="rewrite1.html#R2">are_convertible_wrt</a>  <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="rewrite1.html#T32">REWRITE1:32</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_1_2_2_1_2"><b>case </b></a><a NAME="E1:95_1_1_2_2_1_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">f'</font> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>
 ;<br/><div class="add"><a NAME="E2:95_1_1_2_2_1_2"/>
<font color="Maroon">h'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/><b>then </b><i><font color="Green">E50</font></i>: <font color="Maroon">f</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font></span>)</span> = 
 <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="polynom1.html#D27">POLYNOM1:def 27</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <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>then </b><i><font color="Green">E51</font></i>: <font color="Maroon">f</font> = 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T19">RLVECT_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">h</font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T41">VECTSP_1:41</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1_1_2_2_1_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:95_1_1_2_2_1_2_3"/><i><font color="Green">E52</font></i>: 
 <a href="polynom1.html#K24">-</a> <font color="Maroon">h'</font> <a href="funct_2.html#R2">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>
 ;<br/><i><font color="Green">E53</font></i>:  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h'</font> = 
 <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
<br/>.= 
 <a href="relset_1.html#K4">dom</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="funct_2.html#D1">FUNCT_2:def 1</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="95_1_1_2_2_1_2_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:95_1_1_2_2_1_2_3_2"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h'</font>
 ;<br/><b>then reconsider </b><font color="Maroon">u'</font> = <font color="Maroon">u</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/> <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">h'</font> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">h'</font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font>
<b>by </b><i><a class="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
<b>by </b><i>, <a class="ref" href="polynom1.html#T81">POLYNOM1:81</a></i>
;<br/><b>then </b><font color="Maroon">h'</font> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font> = 
 <a href="rlvect_1.html#K5">-</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#T30">RLVECT_1:30</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#T25">RLVECT_1:25</a></i>
<br/>.= 
<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> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font>
<b>by </b><i><a class="ref" href="polynom1.html#T81">POLYNOM1:81</a></i>
;<br/><b>hence </b><a NAME="E5:95_1_1_2_2_1_2_3_2"/>
<font color="Maroon">h'</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</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> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:95_1_1_2_2_1_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="polyred.html#E6"><i><font color="Green">Lemma72</font></i></a>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div><b>then reconsider </b><font color="Maroon">mh'</font> =  <a href="polynom1.html#K24">-</a> <font color="Maroon">h'</font> as  <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> <b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">mh'</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">x</font> = <font color="Maroon">x</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/><font color="Maroon">h</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">x</font> = 
<font color="Maroon">mh'</font> <a href="polynom1.html#K23">+</a> <font color="Maroon">h'</font>
<b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>
<br/>.= 
 <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font>
<b>by </b><i/>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <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/><a NAME="E10:95_1_1_2_2_1_2"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">mh'</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T19">RLVECT_1:19</a></i>;<br/><a NAME="E11:95_1_1_2_2_1_2"/>
 <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font> <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">mh'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</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="polyred.html#E6"><i><font color="Green">Lemma72</font></i></a>, </i>;<br/><a NAME="E12:95_1_1_2_2_1_2"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">mh'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font>, <a href="polynom1.html#K26">0_</a> <font color="Maroon">n</font>,<font color="Maroon">L</font> <a href="rewrite1.html#R2">are_convertible_wrt</a>  <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#T26">REWRITE1:26</a></i>;<br/><a NAME="E13:95_1_1_2_2_1_2"/>
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">h</font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">mh'</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">p'</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/><b>hence </b><a NAME="E14:95_1_1_2_2_1_2"/>
<font color="Maroon">f</font>,<font color="Maroon">f</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font></span>)</span> <a href="rewrite1.html#R2">are_convertible_wrt</a>  <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font>
 <b>by </b><i>, , , <a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:95_1_1_2"/>
<font color="Maroon">f</font>,<font color="Maroon">f</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font></span>)</span> <a href="rewrite1.html#R2">are_convertible_wrt</a>  <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:95"/>
<font color="Maroon">f</font>,<font color="Maroon">f</font> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K10">*</a> <font color="Maroon">p</font></span>)</span> <a href="rewrite1.html#R2">are_convertible_wrt</a>  <a href="polyred.html#K3" target="_self">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font>
 ;<br/>


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