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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/><b>let </b><font color="Maroon" title="c2">T</font> be  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a> <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a> <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>;<br/><b>let </b><font color="Maroon" title="c3">L</font> be  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a> <a href="vectsp_1.html#V6" title="VECTSP_1:attr.6">right_unital</a> <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">distributive</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">left_unital</a> <a href="vectsp_1.html#V9" title="VECTSP_1:attr.9">Field-like</a> non <a href="realset2.html#V3" title="REALSET2:attr.3">trivial</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c4">p1</font>, <font color="Maroon" title="c5">p2</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/>







<b>assume </b><a NAME="E1:57"/><i><font color="Green" title="E50">A1</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font>, <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> <a href="groeb_2.html#R1" title="GROEB_2:pred.1">are_disjoint</a> 
 ;<br/>

<b>let </b><font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font> be   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font>;<br/>

<b>assume </b><a NAME="E2:57"/>
( <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p1</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c5">p2</font> )
 ;<br/>

<a NAME="E3:57"/><b>then </b>
( <font color="Maroon" title="c6">b1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font> )
 
<b>by </b><i><a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/>
<a NAME="E4:57"/><b>then </b><i><font color="Green" title="E51">A2</font></i>: 
( <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c6">b1</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> &amp; <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c7">b2</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> )
 
<b>by </b><i><a class="ref" href="groeb_3.html#T2" target="_self" title="GROEB_3:th.2">Th2</a></i>;<br/>
<b>assume </b><a NAME="E5:57"/><i><font color="Green" title="E52">A3</font></i>: 
(  not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font> or  not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> )
 ;<br/>

<b>assume </b><a NAME="E6:57"/>
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c6">b1</font>
 ;<br/>

<a NAME="E7:57"/><b>then </b><i><font color="Green" title="E53">A4</font></i>: 
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c7">b2</font> &amp;  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c6">b1</font> )
 
<b>by </b><i><a class="ref" href="polynom1.html#T54" title="POLYNOM1:th.54">POLYNOM1:54</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:57_1_1"/>
(  not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font> or  not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> )
 </span><b>by </b><i><a class="txt" href="groeb_3.html#E5:57"><i><font color="Green" title="E52">A3</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_1_1_1"><b>case </b></a><a NAME="E1:57_1_1_1"/><i><font color="Green" title="E54">A5</font></i>: 
not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font>
 ;<br/><div class="add"><a NAME="E2:57_1_1_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c6">b1</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T54" title="POLYNOM1:th.54">POLYNOM1:54</a></i>;<br/><a NAME="E3:57_1_1_1"/><b>then </b>
 <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c6">b1</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E7:57"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="groeb_2.html#T8" title="GROEB_2:th.8">GROEB_2:8</a></i>;<br/><a NAME="E4:57_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c6">b1</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:57"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="groeb_2.html#T9" title="GROEB_2:th.9">GROEB_2:9</a></i>;<br/><a NAME="E5:57_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T10" title="TERMORD:th.10">TERMORD:10</a></i>;<br/><a NAME="E6:57_1_1_1"/><b>then </b><i><font color="Green" title="E55">A6</font></i>: 
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c6">b1</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E4:57"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="termord.html#T7" title="TERMORD:th.7">TERMORD:7</a></i>;<br/><a NAME="E7:57_1_1_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">-'</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T52" title="POLYNOM1:th.52">POLYNOM1:52</a></i>;<br/><b>hence </b><a NAME="E8:57_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:57_1_1_1"><i><font color="Green" title="E54">A5</font></i></a>, <a class="txt" href="groeb_3.html#E6:57_1_1_1"><i><font color="Green" title="E55">A6</font></i></a>, <a class="ref" href="polynom1.html#T52" title="POLYNOM1:th.52">POLYNOM1:52</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="57_1_1_2"><b>case </b></a><a NAME="E1:57_1_1_2"/><i><font color="Green" title="E54">A7</font></i>: 
not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>
 ;<br/><div class="add"><a NAME="E2:57_1_1_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c7">b2</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T54" title="POLYNOM1:th.54">POLYNOM1:54</a></i>;<br/><a NAME="E3:57_1_1_2"/><b>then </b>
 <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c7">b2</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E7:57"><i><font color="Green" title="E53">A4</font></i></a>, <a class="ref" href="groeb_2.html#T8" title="GROEB_2:th.8">GROEB_2:8</a></i>;<br/><a NAME="E4:57_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#R3" title="POLYNOM1:pred.3">divides</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c7">b2</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:57"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="groeb_2.html#T9" title="GROEB_2:th.9">GROEB_2:9</a></i>;<br/><a NAME="E5:57_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T10" title="TERMORD:th.10">TERMORD:10</a></i>;<br/><a NAME="E6:57_1_1_2"/><b>then </b><i><font color="Green" title="E55">A8</font></i>: 
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <font color="Maroon" title="c7">b2</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E4:57"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="termord.html#T7" title="TERMORD:th.7">TERMORD:7</a></i>;<br/><a NAME="E7:57_1_1_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">-'</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T52" title="POLYNOM1:th.52">POLYNOM1:52</a></i>;<br/><b>hence </b><a NAME="E8:57_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:57_1_1_2"><i><font color="Green" title="E54">A7</font></i></a>, <a class="txt" href="groeb_3.html#E6:57_1_1_2"><i><font color="Green" title="E55">A8</font></i></a>, <a class="ref" href="polynom1.html#T52" title="POLYNOM1:th.52">POLYNOM1:52</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E9:57"/>
contradiction
 ;<br/>


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