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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">T</font> being   <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/>  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="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</a> <br/>  for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</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> holds <br/> ( <font color="Olive" title="b3">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b4">q</font>,<font color="Olive" title="b1">T</font> iff ( ( <font color="Olive" title="b3">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font>) &amp; <font color="Olive" title="b4">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font>) ) or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b1">T</font>),<font color="Olive" title="b1">T</font> or (  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">T</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b1">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Olive" title="b3">p</font>,<font color="Olive" title="b1">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Olive" title="b4">q</font>,<font color="Olive" title="b1">T</font>),<font color="Olive" title="b1">T</font> ) ) )</span><br/><span class="kw">let </span><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>; <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="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</a> <br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</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> holds <br/> ( <font color="Olive" title="b2">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b3">q</font>,<font color="Maroon" title="c2">T</font> iff ( ( <font color="Olive" title="b2">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font>) &amp; <font color="Olive" title="b3">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font>) ) or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b3">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> or (  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b3">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Olive" title="b3">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> ) ) )</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="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L2" title="ALGSTR_0:struct.2">addLoopStr</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>, <font color="Olive" title="b2">q</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> holds <br/> ( <font color="Olive" title="b1">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b2">q</font>,<font color="Maroon" title="c2">T</font> iff ( ( <font color="Olive" title="b1">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>) &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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>) ) or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b2">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> or (  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Olive" title="b2">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Olive" title="b2">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</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"> ( <font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font> iff ( ( <font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>) &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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>) ) or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> or (  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> ) ) )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c6">R</font> =  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #);<br/>
<span class="kw">set </span><font color="Maroon" title="c7">sp</font> =  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">sq</font> =  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">x</font> =  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c10">y</font> =  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>);<br/>
<div><span class="lab"><font color="Green" title="E43">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:52_1"/><span class="lab"><font color="Green" title="E44">A2</font></span>: 
( ( <font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>) &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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>) ) or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> or (  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:52_1_1_1"/>
( ( <font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>) &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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>) ) or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> or (  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1"><span class="lab"><font color="Green" title="E44">A2</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:52_1_1_1_1"/><span class="lab"><font color="Green" title="E45">A3</font></span>: 
( <font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>) &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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>) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font></span><br/><div class="add"><a NAME="E2:52_1_1_1_1"/><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="E3:52_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A4</font></span>: 
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_1"><span class="lab"><font color="Green" title="E45">A3</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E4:52_1_1_1_1"/>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_1"><span class="lab"><font color="Green" title="E45">A3</font></span></a>, <a class="txt" href="polyred.html#E41"><span class="lab"><font color="Green" title="E35">Lm12</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:52_1_1_1_1"/>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52_1_1_1_1"><span class="lab"><font color="Green" title="E46">A4</font></span></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:52_1_1_1_2"/><span class="lab"><font color="Green" title="E45">A5</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">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font></span><br/><div class="add"><a NAME="E2:52_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A6</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">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></span>;<br/><a NAME="E3:52_1_1_1_2"/><span class="lab"><font color="Green" title="E47">A7</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">T</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">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_2"><span class="lab"><font color="Green" title="E45">A5</font></span></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></span>;<br/><a NAME="E4:52_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A8</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><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">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D2" title="TERMORD:def.2">TERMORD:def 2</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:52_1_1_1_2_1_1"/>
(  <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>  or  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:52_1_1_1_2_1_1_1"/><span class="lab"><font color="Green" title="E49">A9</font></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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font></span><br/><div class="add"><a NAME="E2:52_1_1_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A10</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><div><span class="lab"><font color="Green" title="E51">A11</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1_1_1_2_1_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:52_1_1_1_2_1_1_1_1"/>
 <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="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>
 ; <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="E2:52_1_1_1_2_1_1_1_1"/><span class="kw">then </span>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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">q</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E49">A9</font></span></a>, <a class="txt" href="#E2:52_1_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E50">A10</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:52_1_1_1_2_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_2"><span class="lab"><font color="Green" title="E45">A5</font></span></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</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><a NAME="E4:52_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_1_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E50">A10</font></span></a>, <a class="txt" href="polyred.html#E41"><span class="lab"><font color="Green" title="E35">Lm12</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:52_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52_1_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E51">A11</font></span></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:52_1_1_1_2_1_1_2"/><span class="lab"><font color="Green" title="E49">A12</font></span>: 
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font> <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"> <font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font></span><br/><div class="add"><div><span class="lab"><font color="Green" title="E50">A13</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1_1_1_2_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:52_1_1_1_2_1_1_2_1"/>
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font> <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"> contradiction</span><br/><a NAME="E2:52_1_1_1_2_1_1_2_1"/><span class="kw">then </span>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E3:52_1_1_1_2_1_1_2_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bagorder.html#D5" title="BAGORDER:def.5">BAGORDER:def 5</a></span>;<br/><a NAME="E4:52_1_1_1_2_1_1_2_1"/><span class="kw">then </span>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<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> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D2" title="TERMORD:def.2">TERMORD:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:52_1_1_1_2_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52_1_1_1_2"><span class="lab"><font color="Green" title="E47">A7</font></span></a>, <a class="txt" href="#E2:52_1_1_1_2"><span class="lab"><font color="Green" title="E46">A6</font></span></a>, <a class="ref" href="termord.html#T7" title="TERMORD:th.7">TERMORD:7</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><div><span class="lab"><font color="Green" title="E51">A14</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1_1_1_2_1_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:52_1_1_1_2_1_1_2_2"/><span class="lab"><font color="Green" title="E52">A15</font></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="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>
 ; <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="E2:52_1_1_1_2_1_1_2_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E50">A13</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E3:52_1_1_1_2_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A16</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<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> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_2_1_1_2_2"><span class="lab"><font color="Green" title="E52">A15</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E4:52_1_1_1_2_1_1_2_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E49">A12</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E5:52_1_1_1_2_1_1_2_2"/><span class="kw">then </span>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<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> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_2_1_1_2_2"><span class="lab"><font color="Green" title="E52">A15</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><span class="kw">hence </span><a NAME="E6:52_1_1_1_2_1_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_1_1_1_2"><span class="lab"><font color="Green" title="E46">A6</font></span></a>, <a class="txt" href="#E3:52_1_1_1_2_1_1_2_2"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="ref" href="termord.html#T7" title="TERMORD:th.7">TERMORD:7</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><a NAME="E4:52_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="#E1:52_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E49">A12</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E5:52_1_1_1_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">p</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><a NAME="E6:52_1_1_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A17</font></span>: 
 <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <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">p</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>;<br/><a NAME="E7:52_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="#E2:52_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E50">A13</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E8:52_1_1_1_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">q</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><a NAME="E9:52_1_1_1_2_1_1_2"/><span class="kw">then </span>
 <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <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">q</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>;<br/><a NAME="E10:52_1_1_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="bagorder.html#K12" title="BAGORDER:func.12">FinOrd-Approx</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_1_1_1_2"><span class="lab"><font color="Green" title="E46">A6</font></span></a>, <a class="txt" href="#E4:52_1_1_1_2"><span class="lab"><font color="Green" title="E48">A8</font></span></a>, <a class="txt" href="#E1:52_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E49">A12</font></span></a>, <a class="txt" href="#E2:52_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E50">A13</font></span></a>, <a class="txt" href="#E6:52_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E52">A17</font></span></a>, <a class="ref" href="bagorder.html#T35" title="BAGORDER:th.35">BAGORDER:35</a></span>;<br/><a NAME="E11:52_1_1_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bagorder.html#K13" title="BAGORDER:func.13">FinOrd</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bagorder.html#D15" title="BAGORDER:def.15">BAGORDER:def 15</a></span>;<br/><a NAME="E12:52_1_1_1_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></span>;<br/><span class="kw">hence </span><a NAME="E13:52_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E51">A14</font></span></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E6:52_1_1_1_2"/>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 ; <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_3"><span class="kw">case </span></a><a NAME="E1:52_1_1_1_3"/><span class="lab"><font color="Green" title="E45">A18</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">T</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">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font></span><br/><div class="add"><a NAME="E2:52_1_1_1_3"/><span class="kw">then </span>
 <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</a></span>;<br/><a NAME="E3:52_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A19</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bagorder.html#K13" title="BAGORDER:func.13">FinOrd</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1_1_1_3_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_3_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:52_1_1_1_3_1_1"/>
(  <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>  or  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_3_1_1_1"><span class="kw">case </span></a><a NAME="E1:52_1_1_1_3_1_1_1"/>
 <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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:52_1_1_1_3_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A20</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">T</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E3:52_1_1_1_3_1_1_1"/><span class="kw">then </span>
 <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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="polyred.html#E47"><span class="lab"><font color="Green" title="E41">Lm14</font></span></a></span>;<br/><a NAME="E4:52_1_1_1_3_1_1_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#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_3"><span class="lab"><font color="Green" title="E45">A18</font></span></a>, <a class="txt" href="#E2:52_1_1_1_3_1_1_1"><span class="lab"><font color="Green" title="E47">A20</font></span></a>, <a class="txt" href="polyred.html#E47"><span class="lab"><font color="Green" title="E41">Lm14</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:52_1_1_1_3_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_3"><span class="lab"><font color="Green" title="E45">A18</font></span></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_3_1_1_2"><span class="kw">case </span></a><a NAME="E1:52_1_1_1_3_1_1_2"/><span class="lab"><font color="Green" title="E47">A21</font></span>: 
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font> <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"> <font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1_1_1_3_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_3_1_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:52_1_1_1_3_1_1_2_1_1"/>
(  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_3_1_1_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:52_1_1_1_3_1_1_2_1_1_1"/>
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font> <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"> contradiction</span><br/><div class="add"><a NAME="E2:52_1_1_1_3_1_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A22</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E3:52_1_1_1_3_1_1_2_1_1_1"/><span class="kw">then </span>
 <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>) <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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="polyred.html#E47"><span class="lab"><font color="Green" title="E41">Lm14</font></span></a></span>;<br/><a NAME="E4:52_1_1_1_3_1_1_2_1_1_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#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_3"><span class="lab"><font color="Green" title="E45">A18</font></span></a>, <a class="txt" href="#E2:52_1_1_1_3_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E48">A22</font></span></a>, <a class="txt" href="polyred.html#E47"><span class="lab"><font color="Green" title="E41">Lm14</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:52_1_1_1_3_1_1_2_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_3"><span class="lab"><font color="Green" title="E45">A18</font></span></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1_1_3_1_1_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:52_1_1_1_3_1_1_2_1_1_2"/><span class="lab"><font color="Green" title="E48">A23</font></span>: 
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font> <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"> <font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font></span><br/><div class="add"><div><span class="lab"><font color="Green" title="E49">A24</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1_1_1_3_1_1_2_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:52_1_1_1_3_1_1_2_1_1_2_1"/>
 <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="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><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#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_3"><span class="lab"><font color="Green" title="E45">A18</font></span></a>, <a class="ref" href="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>
<br/>.= 
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:52_1_1_1_3_1_1_2_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_3"><span class="lab"><font color="Green" title="E45">A18</font></span></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</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">set </span><font color="Maroon" title="c11">rp</font> =  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>);<br/><span class="kw">set </span><font color="Maroon" title="c12">rq</font> =  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>);<br/><a NAME="E3:52_1_1_1_3_1_1_2_1_1_2"/>
<font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="#E1:52_1_1_1_3_1_1_2"><span class="lab"><font color="Green" title="E47">A21</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E4:52_1_1_1_3_1_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A25</font></span>: 
<font color="Maroon" title="c4">p</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><a NAME="E5:52_1_1_1_3_1_1_2_1_1_2"/>
<font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="#E1:52_1_1_1_3_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E48">A23</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E6:52_1_1_1_3_1_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A26</font></span>: 
<font color="Maroon" title="c5">q</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><a NAME="E7:52_1_1_1_3_1_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A27</font></span>: 
 <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <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">q</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>;<br/><span class="lab"><font color="Green" title="E53">A28</font></span>:  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</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="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</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="txt" href="#E6:52_1_1_1_3_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E51">A26</font></span></a>, <a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>
;<br/> <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</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="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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="txt" href="#E4:52_1_1_1_3_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E50">A25</font></span></a>, <a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>
;<br/><a NAME="E10:52_1_1_1_3_1_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A29</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p5">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p5">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="bagorder.html#K12" title="BAGORDER:func.12">FinOrd-Approx</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52_1_1_1_3"><span class="lab"><font color="Green" title="E46">A19</font></span></a>, <a class="txt" href="#E8:52_1_1_1_3_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E53">A28</font></span></a>, <a class="ref" href="bagorder.html#D15" title="BAGORDER:def.15">BAGORDER:def 15</a></span>;<br/><a NAME="E11:52_1_1_1_3_1_1_2_1_1_2"/>
 <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <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">p</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:52_1_1_1_3_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E50">A25</font></span></a>, <a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>;<br/><a NAME="E12:52_1_1_1_3_1_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="bagorder.html#K12" title="BAGORDER:func.12">FinOrd-Approx</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1_1_3"><span class="lab"><font color="Green" title="E45">A18</font></span></a>, <a class="txt" href="#E1:52_1_1_1_3_1_1_2"><span class="lab"><font color="Green" title="E47">A21</font></span></a>, <a class="txt" href="#E1:52_1_1_1_3_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E48">A23</font></span></a>, <a class="txt" href="#E7:52_1_1_1_3_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E52">A27</font></span></a>, <a class="txt" href="#E10:52_1_1_1_3_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E54">A29</font></span></a>, <a class="ref" href="bagorder.html#T35" title="BAGORDER:th.35">BAGORDER:35</a></span>;<br/><a NAME="E13:52_1_1_1_3_1_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bagorder.html#K13" title="BAGORDER:func.13">FinOrd</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bagorder.html#D15" title="BAGORDER:def.15">BAGORDER:def 15</a></span>;<br/><a NAME="E14:52_1_1_1_3_1_1_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></span>;<br/><span class="kw">hence </span><a NAME="E15:52_1_1_1_3_1_1_2_1_1_2"/>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:52_1_1_1_3_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E49">A24</font></span></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:52_1_1_1_3_1_1_2"/>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 ; <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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:52_1_1_1_3"/>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 ; <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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:52_1"/>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 ; <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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:52_2"/><span class="lab"><font color="Green" title="E44">A30</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>) &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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>) ) or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> or (  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> ) )</span><br/><a NAME="E2:52_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">p</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</a></span>;<br/><a NAME="E3:52_2"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bagorder.html#K13" title="BAGORDER:func.13">FinOrd</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></span>;<br/><a NAME="E4:52_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A31</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="bagorder.html#K12" title="BAGORDER:func.12">FinOrd-Approx</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bagorder.html#D15" title="BAGORDER:def.15">BAGORDER:def 15</a></span>;<br/><a NAME="E5:52_2"/><span class="lab"><font color="Green" title="E46">A32</font></span>: 
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_2"><span class="lab"><font color="Green" title="E44">A30</font></span></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:52_2_1_1"/>
(  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or (  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #) ) or (  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p5">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p5">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="bagorder.html#K12" title="BAGORDER:func.12">FinOrd-Approx</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)</span>)</span></span>)</span> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:52_2"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="bagorder.html#T35" title="BAGORDER:th.35">BAGORDER:35</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:52_2_1_1_1"/>
 <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <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"> ( <font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>) &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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><br/><div class="add"><span class="kw">hence </span><a NAME="E2:52_2_1_1_1"/>
( <font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>) &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="#E5:52_2"><span class="lab"><font color="Green" title="E46">A32</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:52_2_1_1_2"/><span class="lab"><font color="Green" title="E47">A33</font></span>: 
(  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</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#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font></span><br/><div class="add"><a NAME="E2:52_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E3:52_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">q</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><a NAME="E4:52_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A34</font></span>: 
 <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <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">q</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>;<br/><a NAME="E5:52_2_1_1_2"/>
<font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="#E1:52_2_1_1_2"><span class="lab"><font color="Green" title="E47">A33</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E6:52_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">p</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><a NAME="E7:52_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A35</font></span>: 
 <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <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">p</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>;<br/><a NAME="E8:52_2_1_1_2"/><span class="kw">then </span>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<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> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_2_1_1_2"><span class="lab"><font color="Green" title="E47">A33</font></span></a>, <a class="txt" href="#E4:52_2_1_1_2"><span class="lab"><font color="Green" title="E48">A34</font></span></a>, <a class="ref" href="termord.html#D2" title="TERMORD:def.2">TERMORD:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E9:52_2_1_1_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_2_1_1_2"><span class="lab"><font color="Green" title="E47">A33</font></span></a>, <a class="txt" href="#E7:52_2_1_1_2"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="txt" href="#E4:52_2_1_1_2"><span class="lab"><font color="Green" title="E48">A34</font></span></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_2_1_1_3"><span class="kw">case </span></a><a NAME="E1:52_2_1_1_3"/><span class="lab"><font color="Green" title="E47">A36</font></span>: 
(  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p5">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4">(<span class="default"><a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p5">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><a href="bagorder.html#K12" title="BAGORDER:func.12">FinOrd-Approx</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)</span>)</span></span>)</span> )
 ; <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#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> )</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c11">rp</font> =  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>);<br/><span class="kw">set </span><font color="Maroon" title="c12">rq</font> =  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>);<br/><a NAME="E2:52_2_1_1_3"/>
<font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="#E1:52_2_1_1_3"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E3:52_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A37</font></span>: 
<font color="Maroon" title="c4">p</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><a NAME="E4:52_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A38</font></span>: 
 <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <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">p</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>;<br/><a NAME="E5:52_2_1_1_3"/>
<font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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="#E1:52_2_1_1_3"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E6:52_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A39</font></span>: 
<font color="Maroon" title="c5">q</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><a NAME="E7:52_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A40</font></span>: 
 <a href="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <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">q</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>;<br/><div><span class="lab"><font color="Green" title="E52">A41</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="52_2_1_1_3_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:52_2_1_1_3_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_2_1_1_3"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E2:52_2_1_1_3_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>
 <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="E3:52_2_1_1_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A42</font></span>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><a NAME="E4:52_2_1_1_3_1"/>
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</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="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</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="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A43</font></span>: <span class="p1">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> = 
<span class="p1">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</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="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></span>
<br/>.= 
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:52_2_1_1_3_1"><span class="lab"><font color="Green" title="E53">A42</font></span></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></span>
;<br/><a NAME="E6:52_2_1_1_3_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_2_1_1_3"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E7:52_2_1_1_3_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font>
 <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="E8:52_2_1_1_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A44</font></span>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><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">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><a NAME="E9:52_2_1_1_3_1"/>
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</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="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</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="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A45</font></span>: <span class="p1">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> = 
<span class="p1">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</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="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></span>
<br/>.= 
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:52_2_1_1_3_1"><span class="lab"><font color="Green" title="E55">A44</font></span></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></span>
;<br/><span class="kw">assume </span><a NAME="E11:52_2_1_1_3_1"/>
 <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">hence </span><a NAME="E12:52_2_1_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_2"><span class="lab"><font color="Green" title="E44">A30</font></span></a>, <a class="txt" href="#E1:52_2_1_1_3"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="txt" href="#E4:52_2_1_1_3"><span class="lab"><font color="Green" title="E49">A38</font></span></a>, <a class="txt" href="#E7:52_2_1_1_3"><span class="lab"><font color="Green" title="E51">A40</font></span></a>, <a class="txt" href="#E10:52_2_1_1_3_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="txt" href="#E5:52_2_1_1_3_1"><span class="lab"><font color="Green" title="E54">A43</font></span></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</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="lab"><font color="Green" title="E53">A46</font></span>:  <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<font color="Maroon" title="c2">T</font>) = 
<span class="p1">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c4">p</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</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="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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="txt" href="#E3:52_2_1_1_3"><span class="lab"><font color="Green" title="E48">A37</font></span></a>, <a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>
;<br/> <a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<font color="Maroon" title="c2">T</font>) = 
<span class="p1">(<span class="default"><a href="polynom1.html#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c5">q</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</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="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</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="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</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="bagorder.html#K11" title="BAGORDER:func.11">PosetMax</a> <span class="p3">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</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="txt" href="#E6:52_2_1_1_3"><span class="lab"><font color="Green" title="E50">A39</font></span></a>, <a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</a></span>
;<br/><a NAME="E11:52_2_1_1_3"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<span class="p2">(<span class="default"><a href="polyred.html#K2" title="POLYRED:func.2">Support</a> (<span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<font color="Maroon" title="c2">T</font>)</span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bagorder.html#K13" title="BAGORDER:func.13">FinOrd</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_2_1_1_3"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="txt" href="#E9:52_2_1_1_3"><span class="lab"><font color="Green" title="E53">A46</font></span></a>, <a class="ref" href="bagorder.html#D15" title="BAGORDER:def.15">BAGORDER:def 15</a></span>;<br/><a NAME="E12:52_2_1_1_3"/><span class="kw">then </span>
 <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></span>;<br/><span class="kw">hence </span><a NAME="E13:52_2_1_1_3"/>
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_2_1_1_3"><span class="lab"><font color="Green" title="E47">A36</font></span></a>, <a class="txt" href="#E6:52_2_1_1_3"><span class="lab"><font color="Green" title="E50">A39</font></span></a>, <a class="txt" href="#E4:52_2_1_1_3"><span class="lab"><font color="Green" title="E49">A38</font></span></a>, <a class="txt" href="#E8:52_2_1_1_3"><span class="lab"><font color="Green" title="E52">A41</font></span></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</a>, <a class="ref" href="polyred.html#T24" target="_self" title="POLYRED:th.24">Th24</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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E7:52_2"/>
( ( <font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>) &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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>) ) or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> or (  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> ) )
 ; <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="E3:52"/>
( <font color="Maroon" title="c4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font> iff ( ( <font color="Maroon" title="c4">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>) &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</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>) ) or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> or (  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</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">q</font>,<font color="Maroon" title="c2">T</font>) &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c2">T</font>) <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> (<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E43">A1</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>
