<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/><b>let </b><font color="Maroon" title="c2">T</font> be  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a> <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a> <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>;<br/><b>let </b><font color="Maroon" title="c3">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> <a href="group_1.html#V6" title="GROUP_1:attr.6">commutative</a> <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">well-unital</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">distributive</a> <a href="vectsp_1.html#NV11" title="VECTSP_1:NV.11">Field-like</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c6">g</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/>







<b>set </b><font color="Maroon" title="c7">R</font> =  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #);<br/>
<b>assume </b><a NAME="E1:75"/><i><font color="Green" title="E58">A1</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c2">T</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c8">b</font> being   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E3:75"/><i><font color="Green" title="E59">A2</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a> <font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c8">b</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D6" target="_self" title="POLYRED:def.6">Def6</a></i>;<br/>
<a NAME="E4:75"/>
<font color="Maroon" title="c8">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E3:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self" title="POLYRED:def.5">Def5</a></i>;<br/>
<a NAME="E5:75"/><b>then </b><i><font color="Green" title="E60">A3</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">g</font>
 
<b>by </b><i><a class="txt" href="polyred.html#E3:75"><i><font color="Green" title="E59">A2</font></i></a>, <a class="txt" href="polyred.html#E65"><i><font color="Green" title="E52">Lm17</font></i></a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b>for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">g</font> being  <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  st  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp; <font color="Olive" title="b1">f</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Olive" title="b3">g</font>,<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">T</font> holds <br/><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#K12" title="POLYNOM1:func.12">Support</a> <font color="Olive" title="b3">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Olive" title="b1">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #);<br/>
<a NAME="E6:75"/><i><font color="Green" title="E61">A4</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">f</font>, <font color="Maroon" title="c10">p</font>, <font color="Maroon" title="c11">g</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/>

<b>assume </b><a NAME="E1:75_1"/><i><font color="Green" title="E62">A5</font></i>: 
(  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c9">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; <font color="Maroon" title="c9">f</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Maroon" title="c11">g</font>,<font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c2">T</font> )
 ;<br/>

<a NAME="E2:75_1"/><b>then </b>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c9">f</font>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">are_equipotent</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#D5" title="CARD_1:def.5">CARD_1:def 5</a></i>;<br/>
<a NAME="E3:75_1"/><b>then </b>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c9">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T46" title="CARD_1:th.46">CARD_1:46</a></i>;<br/>
<a NAME="E4:75_1"/><b>then </b>
<font color="Maroon" title="c9">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 
<b>by </b><i><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></i>;<br/>
<a NAME="E5:75_1"/><b>then </b>
<font color="Maroon" title="c9">f</font> <a href="polyred.html#NR7" title="POLYRED:NR.7">is_irreducible_wrt</a> <font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="ref" href="polyred.html#T37" target="_self" title="POLYRED:th.37">Th37</a></i>;<br/>
<b>hence </b><a NAME="E6:75_1"/>
<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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c11">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c9">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_1"><i><font color="Green" title="E62">A5</font></i></a>, <a class="ref" href="polyred.html#D8" target="_self" title="POLYRED:def.8">Def8</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:75"/><i><font color="Green" title="E62">A6</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:75_2"/><i><font color="Green" title="E63">A7</font></i>: 
for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">g</font> being  <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  st  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">k</font> &amp; <font color="Olive" title="b1">f</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Olive" title="b3">g</font>,<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">T</font> holds <br/><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#K12" title="POLYNOM1:func.12">Support</a> <font color="Olive" title="b3">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Olive" title="b1">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c10">f</font>, <font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c12">g</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>;<br/><b>assume </b><a NAME="E1:75_2_1"/><i><font color="Green" title="E64">A8</font></i>: 
(  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 &amp; <font color="Maroon" title="c10">f</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font> )
 ;<br/><b>then consider </b><font color="Maroon" title="c13">b</font> being   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E3:75_2_1"/><i><font color="Green" title="E65">A9</font></i>: 
<font color="Maroon" title="c10">f</font> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c13">b</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D6" target="_self" title="POLYRED:def.6">Def6</a></i>;<br/><b>consider </b><font color="Maroon" title="c14">s</font> being   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">bag</a> of <font color="Maroon" title="c1">n</font><b> such that </b><br/><a NAME="E5:75_2_1"/><i><font color="Green" title="E66">A10</font></i>: 
( <font color="Maroon" title="c14">s</font> <a href="polynom1.html#K9" title="POLYNOM1:func.9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b</font> &amp; <font color="Maroon" title="c12">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c10">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green" title="E65">A9</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self" title="POLYRED:def.5">Def5</a></i>;<br/><a NAME="E6:75_2_1"/><i><font color="Green" title="E67">A11</font></i>: 
<font color="Maroon" title="c13">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</font>
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green" title="E65">A9</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self" title="POLYRED:def.5">Def5</a></i>;<br/><a NAME="E7:75_2_1"/><i><font color="Green" title="E68">A12</font></i>: 
<font color="Maroon" title="c2">T</font> <a href="relat_2.html#R6" title="RELAT_2:pred.6">is_connected_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="relat_2.html#D14" title="RELAT_2:def.14">RELAT_2:def 14</a></i>;<br/><a NAME="E8:75_2_1"/><i><font color="Green" title="E69">A13</font></i>: 
<font color="Maroon" title="c10">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green" title="E65">A9</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self" title="POLYRED:def.5">Def5</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:75_2_1_1_1"/>
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c10">f</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="c12">g</font>,<font color="Maroon" title="c2">T</font> or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</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="c10">f</font>,<font color="Maroon" title="c2">T</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_2_1_1_1_1"><b>case </b></a><a NAME="E1:75_2_1_1_1_1"/><i><font color="Green" title="E70">A14</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c10">f</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="c12">g</font>,<font color="Maroon" title="c2">T</font>
 ;<br/><div class="add"><a NAME="E2:75_2_1_1_1_1"/>
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c10">f</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="c10">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</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="c12">g</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font> )
 <b>by </b><i><a class="ref" href="termord.html#T6" title="TERMORD:th.6">TERMORD:6</a></i>;<br/><a NAME="E3:75_2_1_1_1_1"/><b>then </b>
( <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="c10">f</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="c10">f</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> &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="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</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="c12">g</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> )
 <b>by </b><i><a class="ref" href="termord.html#D2" title="TERMORD:def.2">TERMORD:def 2</a></i>;<br/><a NAME="E4:75_2_1_1_1_1"/><b>then </b>
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c2">T</font> &amp;  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c2">T</font> )
 <b>by </b><i><a class="ref" href="relat_1.html#T30" title="RELAT_1:th.30">RELAT_1:30</a></i>;<br/><a NAME="E5:75_2_1_1_1_1"/><b>then </b><i><font color="Green" title="E71">A15</font></i>: 
( <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="c10">f</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="c12">g</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> or <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="c12">g</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="c10">f</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> )
 <b>by </b><i><a class="txt" href="polyred.html#E7:75_2_1"><i><font color="Green" title="E68">A12</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_1"><i><font color="Green" title="E70">A14</font></i></a>, <a class="ref" href="relat_2.html#D6" title="RELAT_2:def.6">RELAT_2:def 6</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2_1_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_2_1_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:75_2_1_1_1_1_1_1"/>
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c10">f</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="c12">g</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="c12">g</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="c10">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font> )
 </span><b>by </b><i><a class="txt" href="polyred.html#E5:75_2_1_1_1_1"><i><font color="Green" title="E71">A15</font></i></a>, <a class="ref" href="termord.html#D2" title="TERMORD:def.2">TERMORD:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_2_1_1_1_1_1_1_1"><b>case </b></a><a NAME="E1:75_2_1_1_1_1_1_1_1"/><i><font color="Green" title="E72">A16</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c10">f</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="c12">g</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2_1_1_1_1_1_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:75_2_1_1_1_1_1_1_1_1"/>
not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c12">g</font>
 ;<br/><a NAME="E2:75_2_1_1_1_1_1_1_1_1"/><b>then </b>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><a NAME="E3:75_2_1_1_1_1_1_1_1_1"/><b>then </b>
<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="c12">g</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="c10">f</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>
 <b>by </b><i><a class="ref" href="bagorder.html#D7" title="BAGORDER:def.7">BAGORDER:def 7</a></i>;<br/><a NAME="E4:75_2_1_1_1_1_1_1_1_1"/><b>then </b>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</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="c10">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="termord.html#D2" title="TERMORD:def.2">TERMORD:def 2</a></i>;<br/><b>hence </b><a NAME="E5:75_2_1_1_1_1_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1_1_1_1"><i><font color="Green" title="E70">A14</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_1_1_1_1"><i><font color="Green" title="E72">A16</font></i></a>, <a class="ref" href="termord.html#T7" title="TERMORD:th.7">TERMORD:7</a></i>;<br/></div><b>end;</b></div><a NAME="E3:75_2_1_1_1_1_1_1_1"/><b>then </b>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</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="c10">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1"><i><font color="Green" title="E64">A8</font></i></a>, <a class="ref" href="polyred.html#T42" target="_self" title="POLYRED:th.42">Th42</a></i>;<br/><b>hence </b><a NAME="E4:75_2_1_1_1_1_1_1_1"/>
<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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c12">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1_1_1_1"><i><font color="Green" title="E70">A14</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_1_1_1_1"><i><font color="Green" title="E72">A16</font></i></a>, <a class="ref" href="termord.html#T7" title="TERMORD:th.7">TERMORD:7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_2_1_1_1_1_1_1_2"><b>case </b></a><a NAME="E1:75_2_1_1_1_1_1_1_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</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="c10">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 ;<br/><div class="add"><a NAME="E2:75_2_1_1_1_1_1_1_2"/><b>then </b>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</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="c10">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1_1_1_1"><i><font color="Green" title="E70">A14</font></i></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></i>;<br/><a NAME="E3:75_2_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c12">g</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E48"><i><font color="Green" title="E42">Lm15</font></i></a></i>;<br/><a NAME="E4:75_2_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c12">g</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</a></i>;<br/><b>hence </b><a NAME="E5:75_2_1_1_1_1_1_1_2"/>
<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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c12">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <b>by </b><i><a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E7:75_2_1_1_1_1"/>
<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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c12">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_2_1_1_1_2"><b>case </b></a><a NAME="E1:75_2_1_1_1_2"/><i><font color="Green" title="E70">A17</font></i>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</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="c10">f</font>,<font color="Maroon" title="c2">T</font>
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_2_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:75_2_1_1_1_2_1_1"/>
( <font color="Maroon" title="c13">b</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="c10">f</font>,<font color="Maroon" title="c2">T</font> or <font color="Maroon" title="c13">b</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="c10">f</font>,<font color="Maroon" title="c2">T</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_2_1_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:75_2_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c13">b</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="c10">f</font>,<font color="Maroon" title="c2">T</font>
 ;<br/><div class="add"><a NAME="E2:75_2_1_1_1_2_1_1_1"/><b>then </b>
not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c12">g</font>
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_2"><i><font color="Green" title="E70">A17</font></i></a>, <a class="txt" href="polyred.html#E65"><i><font color="Green" title="E52">Lm17</font></i></a></i>;<br/><a NAME="E3:75_2_1_1_1_2_1_1_1"/><b>then </b>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c12">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><a NAME="E4:75_2_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c12">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></i>;<br/><a NAME="E5:75_2_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c12">g</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E41"><i><font color="Green" title="E35">Lm12</font></i></a></i>;<br/><b>hence </b><a NAME="E6:75_2_1_1_1_2_1_1_1"/>
<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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c12">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <b>by </b><i><a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="75_2_1_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:75_2_1_1_1_2_1_1_2"/><i><font color="Green" title="E71">A18</font></i>: 
<font color="Maroon" title="c13">b</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="c10">f</font>,<font color="Maroon" title="c2">T</font>
 ;<br/><div class="add"><a NAME="E2:75_2_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c13">b</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="c10">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E6:75_2_1"><i><font color="Green" title="E67">A11</font></i></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><a NAME="E3:75_2_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c13">b</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="c10">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E71">A18</font></i></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></i>;<br/><a NAME="E4:75_2_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c10">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green" title="E65">A9</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_2"><i><font color="Green" title="E70">A17</font></i></a>, <a class="ref" href="polyred.html#T41" target="_self" title="POLYRED:th.41">Th41</a></i>;<br/><b>then </b> <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font> = 
<font color="Maroon" title="c12">g</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></i>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font>
<b>by </b><i><a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></i>
;<br/><b>then </b><i><font color="Green" title="E72">A19</font></i>:  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font> = 
 <a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1_1_1_2"><i><font color="Green" title="E70">A17</font></i></a>, <a class="ref" href="termord.html#D8" title="TERMORD:def.8">TERMORD:def 8</a></i>
<br/>.= 
 <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font>
<b>by </b><i><a class="ref" href="termord.html#D8" title="TERMORD:def.8">TERMORD:def 8</a></i>
;<br/><a NAME="E7:75_2_1_1_1_2_1_1_2"/><i><font color="Green" title="E73">A20</font></i>: 
not <font color="Maroon" title="c13">b</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="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E71">A18</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E8:75_2_1_1_1_2_1_1_2"/><i><font color="Green" title="E74">A21</font></i>: 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c10">f</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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</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="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></i>;<br/><a NAME="E9:75_2_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E75">A22</font></i>: 
<font color="Maroon" title="c13">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E6:75_2_1"><i><font color="Green" title="E67">A11</font></i></a>, <a class="txt" href="polyred.html#E7:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E73">A20</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E10:75_2_1_1_1_2_1_1_2"/><b>then </b>
 <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <b>by </b><i><a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c15">rf</font> =  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font> as  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <b>by </b><i><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></i>;<br/><a NAME="E12:75_2_1_1_1_2_1_1_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</font>
 <b>by </b><i><a class="txt" href="polyred.html#E6:75_2_1"><i><font color="Green" title="E67">A11</font></i></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></i>;<br/><a NAME="E13:75_2_1_1_1_2_1_1_2"/><b>then </b>
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="c10">f</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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E14:75_2_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E76">A23</font></i>: 
<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="c10">f</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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/><i><font color="Green" title="E77">A24</font></i>: <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c10">f</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="c10">f</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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</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="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="txt" href="polyred.html#E8:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E74">A21</font></i></a>, <a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
<br/>.= 
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</font>
<b>by </b><i><a class="txt" href="polyred.html#E14:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E76">A23</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
;<br/><a NAME="E16:75_2_1_1_1_2_1_1_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</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="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E17:75_2_1_1_1_2_1_1_2"/><b>then </b>
not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E8:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E74">A21</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E18:75_2_1_1_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1"><i><font color="Green" title="E64">A8</font></i></a>, <a class="txt" href="polyred.html#E15:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E77">A24</font></i></a>, <a class="ref" href="card_2.html#T54" title="CARD_2:th.54">CARD_2:54</a></i>;<br/><a NAME="E19:75_2_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E78">A25</font></i>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">k</font>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T2" title="XCMPLX_1:th.2">XCMPLX_1:2</a></i>;<br/><a NAME="E20:75_2_1_1_1_2_1_1_2"/><i><font color="Green" title="E79">A26</font></i>: 
( <font color="Maroon" title="c15">rf</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c11">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green" title="E65">A9</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self" title="POLYRED:def.5">Def5</a>, <a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></i>;<br/> <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">f</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="txt" href="polyred.html#E5:75_2_1"><i><font color="Green" title="E66">A10</font></i></a>, <a class="txt" href="polyred.html#E6:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E72">A19</font></i></a>, <a class="ref" href="termord.html#D9" title="TERMORD:def.9">TERMORD:def 9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <font color="Maroon" title="c15">rf</font></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">f</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T38" title="TERMORD:th.38">TERMORD:38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <font color="Maroon" title="c15">rf</font></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="txt" href="polyred.html#E6:75_2_1"><i><font color="Green" title="E67">A11</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E71">A18</font></i></a>, <a class="ref" href="termord.html#T40" title="TERMORD:th.40">TERMORD:40</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <font color="Maroon" title="c15">rf</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24" title="POLYNOM1:func.24">-</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23" title="POLYNOM1:func.23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T83" title="POLYNOM1:th.83">POLYNOM1:83</a></i>
<br/>.= 
<font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K25" title="POLYNOM1:func.25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c15">rf</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">b</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">s</font> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c11">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T82" title="POLYNOM1:th.82">POLYNOM1:82</a></i>
;<br/><a NAME="E22:75_2_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c15">rf</font> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c13">b</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E5:75_2_1"><i><font color="Green" title="E66">A10</font></i></a>, <a class="txt" href="polyred.html#E9:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E75">A22</font></i></a>, <a class="txt" href="polyred.html#E20:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E79">A26</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self" title="POLYRED:def.5">Def5</a></i>;<br/><a NAME="E23:75_2_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c15">rf</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a>  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D6" target="_self" title="POLYRED:def.6">Def6</a></i>;<br/><a NAME="E24:75_2_1_1_1_2_1_1_2"/><b>then </b>
<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#K12" title="POLYNOM1:func.12">Support</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c15">rf</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2"><i><font color="Green" title="E63">A7</font></i></a>, <a class="txt" href="polyred.html#E19:75_2_1_1_1_2_1_1_2"><i><font color="Green" title="E78">A25</font></i></a></i>;<br/><a NAME="E25:75_2_1_1_1_2_1_1_2"/><b>then </b>
 <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c12">g</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="c10">f</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></i>;<br/><a NAME="E26:75_2_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c12">g</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E8:75_2_1"><i><font color="Green" title="E69">A13</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_2"><i><font color="Green" title="E70">A17</font></i></a>, <a class="txt" href="polyred.html#E50"><i><font color="Green" title="E43">Lm16</font></i></a></i>;<br/><b>hence </b><a NAME="E27:75_2_1_1_1_2_1_1_2"/>
<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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c12">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 <b>by </b><i><a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:75_2_1_1_1_2"/>
<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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c12">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E10:75_2_1"/>
<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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c12">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:75_2"/>
for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">g</font> being  <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  st  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">k</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 &amp; <font color="Olive" title="b1">f</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Olive" title="b3">g</font>,<font color="Olive" title="b2">p</font>,<font color="Maroon" title="c2">T</font> holds <br/><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#K12" title="POLYNOM1:func.12">Support</a> <font color="Olive" title="b3">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Olive" title="b1">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 ;<br/>


</div><b>end;</b></div>
<a NAME="E8:75"/><i><font color="Green" title="E63">A27</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="polyred.html#E6:75"><i><font color="Green" title="E61">A4</font></i></a>, <a class="txt" href="polyred.html#E7:75"><i><font color="Green" title="E62">A6</font></i></a>);<br/></i>
<b>consider </b><font color="Maroon" title="c9">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E10:75"/><i><font color="Green" title="E64">A28</font></i>: 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">k</font>
 ;<br/>
<a NAME="E11:75"/>
<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#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c6">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c4">f</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="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c2">T</font> #)
 
<b>by </b><i><a class="txt" href="polyred.html#E1:75"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="polyred.html#E8:75"><i><font color="Green" title="E63">A27</font></i></a>, <a class="txt" href="polyred.html#E10:75"><i><font color="Green" title="E64">A28</font></i></a></i>;<br/>
<a NAME="E12:75"/><b>then </b>
<font color="Maroon" title="c6">g</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">T</font>
 
<b>by </b><i><a class="ref" href="polyred.html#D2" target="_self" title="POLYRED:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E13:75"/>
<font color="Maroon" title="c6">g</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c2">T</font>
 <b>by </b><i><a class="txt" href="polyred.html#E5:75"><i><font color="Green" title="E60">A3</font></i></a>, <a class="ref" href="polyred.html#D3" target="_self" title="POLYRED:def.3">Def3</a></i>;<br/>


</div>
