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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#V2" title="STRUCT_0:attr.2">empty</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="rlvect_1.html#L1" title="RLVECT_1:struct.1">LoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c4">p</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>let </b><font color="Maroon" title="c5">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>









<b>assume </b><a NAME="E1:51"/><i><font color="Green" title="E42">A1</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p</font></span>)</span>
 ;<br/>

<a NAME="E2:51"/><b>then </b><i><font color="Green" title="E43">A2</font></i>: 
<font color="Maroon" title="c5">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p</font></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E3:51"/><b>then </b><i><font color="Green" title="E44">A3</font></i>: 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">l</font> =  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c5">i</font>;<br/>
<b>set </b><font color="Maroon" title="c7">l1</font> =  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<a NAME="E4:51"/><i><font color="Green" title="E45">A4</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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">p</font>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E2:51"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="groeb_3.html#T26" target="_self" title="GROEB_3:th.26">Th26</a></i>;<br/>
<a NAME="E5:51"/><i><font color="Green" title="E46">A5</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c5">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="groeb_3.html#K4" title="GROEB_3:func.4">Lower_Support</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c5">i</font>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:51"><i><font color="Green" title="E42">A1</font></i></a>, <a class="txt" href="groeb_3.html#E32"><i><font color="Green" title="E25">Lm3</font></i></a></i>;<br/>
<a NAME="E6:51"/><b>then </b><i><font color="Green" title="E47">A6</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c5">i</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">p</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">i</font>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:51"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="groeb_3.html#T24" target="_self" title="GROEB_3:th.24">Th24</a></i>;<br/>
<a NAME="E7:51"/><i><font color="Green" title="E48">A7</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:51"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="groeb_3.html#T38" target="_self" title="GROEB_3:th.38">Th38</a></i>;<br/>
<a NAME="E8:51"/><i><font color="Green" title="E49">A8</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="groeb_3.html#K4" title="GROEB_3:func.4">Lower_Support</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c5">i</font>
 
<b>by </b><i><a class="txt" href="groeb_3.html#E3:51"><i><font color="Green" title="E44">A3</font></i></a>, <a class="txt" href="groeb_3.html#E5:51"><i><font color="Green" title="E46">A5</font></i></a>, <a class="txt" href="groeb_3.html#E6:51"><i><font color="Green" title="E47">A6</font></i></a>, <a class="ref" href="card_1.html#T78" title="CARD_1:th.78">CARD_1:78</a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">u'</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:51_1"/><i><font color="Green" title="E50">A9</font></i>: 
<font color="Maroon" title="c8">u'</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="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c9">u</font> = <font color="Maroon" title="c8">u'</font> as    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font> ;<br/><a NAME="E3:51_1"/>
<font color="Maroon" title="c9">u</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:51_1"><i><font color="Green" title="E50">A9</font></i></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><a NAME="E4:51_1"/><b>then </b>
<font color="Maroon" title="c9">u</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c5">i</font></span>)</span>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E7:51"><i><font color="Green" title="E48">A7</font></i></a>, <a class="ref" href="termord.html#T8" title="TERMORD:th.8">TERMORD:8</a></i>;<br/><b>hence </b><a NAME="E5:51_1"/>
<font color="Maroon" title="c8">u'</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="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c5">i</font></span>)</span>
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:51"><i><font color="Green" title="E42">A1</font></i></a>, <a class="txt" href="groeb_3.html#E4:51"><i><font color="Green" title="E45">A4</font></i></a>, <a class="txt" href="groeb_3.html#E5:51"><i><font color="Green" title="E46">A5</font></i></a>, <a class="txt" href="groeb_3.html#E8:51"><i><font color="Green" title="E49">A8</font></i></a>, <a class="txt" href="groeb_3.html#E1:51_1"><i><font color="Green" title="E50">A9</font></i></a>, <a class="ref" href="groeb_3.html#T24" target="_self" title="GROEB_3:th.24">Th24</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:51"/>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c5">i</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>


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