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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/><b>let </b><font color="Maroon" title="c2">T</font> be  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a> <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a> <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>;<br/><b>let </b><font color="Maroon" title="c3">L</font> be  non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> <a href="group_1.html#V6" title="GROUP_1:attr.6">commutative</a> <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">well-unital</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">distributive</a> <a href="vectsp_1.html#NV11" title="VECTSP_1:NV.11">Field-like</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="E1:64"/><i><font color="Green" title="E53">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="E2:64"/><i><font color="Green" title="E54">A2</font></i>: 
( <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> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> &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> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> )
 ;<br/>

<a NAME="E3:64"/><i><font color="Green" title="E55">A3</font></i>: 
(  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p1</font> &amp;  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c5">p2</font> )
 
<b>by </b><i><a class="ref" href="termord.html#T35" title="TERMORD:th.35">TERMORD:35</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="64_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:64_1"/>
<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/><a NAME="E2:64_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="termord.html#T39" title="TERMORD:th.39">TERMORD:39</a></i>;<br/><b>hence </b><a NAME="E3:64_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_3.html#E2:64"><i><font color="Green" title="E54">A2</font></i></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:64"/>
not <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>
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:64"><i><font color="Green" title="E53">A1</font></i></a>, <a class="txt" href="groeb_3.html#E2:64"><i><font color="Green" title="E54">A2</font></i></a>, <a class="txt" href="groeb_3.html#E3:64"><i><font color="Green" title="E55">A3</font></i></a>, <a class="txt" href="groeb_3.html#E55"><i><font color="Green" title="E47">Lm5</font></i></a></i>;<br/>


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