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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">O</font> being   <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>  <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font><br/>  for <font color="Olive" title="b2">L</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="struct_0.html#L2" title="STRUCT_0:struct.2">ZeroStr</a> <br/>  for <font color="Olive" title="b3">p</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font>  st  <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">O</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="Olive" title="b2">L</font> holds <br/> <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">O</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">O</font> be   <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>  <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="struct_0.html#L2" title="STRUCT_0:struct.2">ZeroStr</a> <br/>  for <font color="Olive" title="b2">p</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font>  st  <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">O</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="Olive" title="b1">L</font> holds <br/> <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">L</font> be   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="struct_0.html#L2" title="STRUCT_0:struct.2">ZeroStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  st  <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">O</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> holds <br/> <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font> be   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</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> implies  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>







<span class="kw">assume </span><a NAME="E1:37"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E2:37"/><span class="kw">then </span>
<font color="Maroon" title="c4">p</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="termord.html#E31"><span class="lab"><font color="Green" title="E22">Lm7</font></span></a></span>;<br/>
<a NAME="E3:37"/><span class="kw">then </span>
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/>
<a NAME="E4:37"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A2</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D6" target="_self" title="TERMORD:def.6">Def6</a></span>;<br/>
<a NAME="E5:37"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="polynom7.html#T8" title="POLYNOM7:th.8">POLYNOM7:8</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:37_1"/>
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:37_1"/><span class="kw">then </span>
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T7" title="POLYNOM7:th.7">POLYNOM7:7</a></span>;<br/><a NAME="E3:37_1"/><span class="kw">then </span>
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E4:37_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="ref" href="polynom1.html#D3" title="POLYNOM1:def.3">POLYNOM1:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E5:37_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="txt" href="termord.html#E32"><span class="lab"><font color="Green" title="E23">Lm8</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E7:37"/>
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">O</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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