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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="relat_2.html#V6">connected</a> <a href="bagorder.html#V2">admissible</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V2">unital</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V9">Field-like</a> non <a href="vectsp_1.html#V10">degenerated</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #);<br/>
<b>assume </b><a NAME="E1:75"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="polyred.html#R4" target="_self">reduces_to</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:75"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="polyred.html#R3" target="_self">reduces_to</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="polyred.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E4:75"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="polyred.html#E3:75"><i><font color="Green">E59</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E5:75"/><b>then </b><i><font color="Green">E60</font></i>: 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="polyred.html#E3:75"><i><font color="Green">E59</font></i></a>, <a class="txt" href="polyred.html#E65"><i><font color="Green">Lemma52</font></i></a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> st  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="polyred.html#R4" target="_self">reduces_to</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #);<br/>
<a NAME="E6:75"/><i><font color="Green">E61</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">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>

<b>assume </b><a NAME="E1:75_1"/><i><font color="Green">E62</font></i>: 
(  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>9</sub></font> <a href="polyred.html#R4" target="_self">reduces_to</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:75_1"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>9</sub></font>, <a href="xboole_0.html#K1">{}</a>  <a href="tarski.html#R2">are_equipotent</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a></i>;<br/>
<a NAME="E3:75_1"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T46">CARD_1:46</a></i>;<br/>
<a NAME="E4:75_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#R2">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/>
<a NAME="E5:75_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="polyred.html#NR7" target="_self">is_irreducible_wrt</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="polyred.html#T37" target="_self">Th37</a></i>;<br/>
<b>hence </b><a NAME="E6:75_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #)
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="polyred.html#D8" target="_self">Def8</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:75"/><i><font color="Green">E62</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</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">c<sub>9</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:75_2"/><i><font color="Green">E63</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> st  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="polyred.html#R4" target="_self">reduces_to</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></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">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>assume </b><a NAME="E1:75_2_1"/><i><font color="Green">E64</font></i>: 
(  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>10</sub></font> <a href="polyred.html#R4" target="_self">reduces_to</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 ;<br/><b>then consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:75_2_1"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="polyred.html#R3" target="_self">reduces_to</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="polyred.html#D6" target="_self">Def6</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:75_2_1"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="polynom1.html#K9">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E6:75_2_1"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E7:75_2_1"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R6">is_connected_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="relat_2.html#D14">RELAT_2:def 14</a></i>;<br/><a NAME="E8:75_2_1"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self">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">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> or  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></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">E70</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:75_2_1_1_1_1"/>
(  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="termord.html#T6">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">[</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="termord.html#D2">TERMORD:def 2</a></i>;<br/><a NAME="E4:75_2_1_1_1_1"/><b>then </b>
(  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="relat_1.html#T30">RELAT_1:30</a></i>;<br/><a NAME="E5:75_2_1_1_1_1"/><b>then </b><i><font color="Green">E71</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="polyred.html#E7:75_2_1"><i><font color="Green">E68</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="relat_2.html#D6">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">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> or  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 </span><b>by </b><i><a class="txt" href="polyred.html#E5:75_2_1_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="termord.html#D2">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">E72</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></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">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>12</sub></font>
 ;<br/><a NAME="E2:75_2_1_1_1_1_1_1_1_1"/><b>then </b>
 <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K16">EmptyBag</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="termord.html#D6">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">[</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="bagorder.html#D7">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">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="termord.html#D2">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">E70</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_1_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="termord.html#T7">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">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="polyred.html#T42" target="_self">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">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #)
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1_1_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_1_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="termord.html#T7">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">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></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">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="termord.html#R2">&lt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1_1_1_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/><a NAME="E3:75_2_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="polyred.html#R2" target="_self">&lt;</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E48"><i><font color="Green">Lemma42</font></i></a></i>;<br/><a NAME="E4:75_2_1_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="polyred.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="polyred.html#D3" target="_self">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">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #)
 <b>by </b><i><a class="ref" href="polyred.html#D2" target="_self">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">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></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">E70</font></i>: 
 <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></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">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></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">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green">E65</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="polyred.html#E65"><i><font color="Green">Lemma52</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">Support</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E4:75_2_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="funct_2.html#R2">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/><a NAME="E5:75_2_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="polyred.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E41"><i><font color="Green">Lemma35</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">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #)
 <b>by </b><i><a class="ref" href="polyred.html#D2" target="_self">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">E71</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:75_2_1_1_1_2_1_1_2"/>
<font color="Maroon">c<sub>13</sub></font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E6:75_2_1"><i><font color="Green">E67</font></i></a>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/><a NAME="E3:75_2_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="termord.html#R2">&lt;</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></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">E71</font></i></a>, <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/><a NAME="E4:75_2_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green">E65</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="polyred.html#T41" target="_self">Th41</a></i>;<br/><b>then </b> <a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
<font color="Maroon">c<sub>12</sub></font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>
<br/>.= 
 <a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="termord.html#D7">TERMORD:def 7</a></i>
;<br/><b>then </b><i><font color="Green">E72</font></i>:  <a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="polynom7.html#K1">Monom</a> <span class="p1">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="ref" href="termord.html#D8">TERMORD:def 8</a></i>
<br/>.= 
 <a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="termord.html#D8">TERMORD:def 8</a></i>
;<br/><a NAME="E7:75_2_1_1_1_2_1_1_2"/><i><font color="Green">E73</font></i>: 
not <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</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">E71</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E8:75_2_1_1_1_2_1_1_2"/><i><font color="Green">E74</font></i>: 
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="termord.html#T36">TERMORD:36</a></i>;<br/><a NAME="E9:75_2_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polyred.html#E6:75_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="polyred.html#E7:75_2_1_1_1_2_1_1_2"><i><font color="Green">E73</font></i></a>, <a class="ref" href="xboole_0.html#D4">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">Red</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>15</sub></font> =  <a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> as  <a href="polynom7.html#V1">non-zero</a> <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/><a NAME="E12:75_2_1_1_1_2_1_1_2"/>
 <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E6:75_2_1"><i><font color="Green">E67</font></i></a>, <a class="ref" href="termord.html#D6">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">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">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">E76</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/><i><font color="Green">E77</font></i>: <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> = 
<span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</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">E74</font></i></a>, <a class="ref" href="xboole_1.html#T39">XBOOLE_1:39</a></i>
<br/>.= 
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></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">E76</font></i></a>, <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><a NAME="E16:75_2_1_1_1_2_1_1_2"/>
 <a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">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">HT</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></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">E74</font></i></a>, <a class="ref" href="xboole_0.html#D4">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">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2_1"><i><font color="Green">E64</font></i></a>, <a class="txt" href="polyred.html#E15:75_2_1_1_1_2_1_1_2"><i><font color="Green">E77</font></i></a>, <a class="ref" href="card_2.html#T54">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">E78</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T2">XCMPLX_1:2</a></i>;<br/><a NAME="E20:75_2_1_1_1_2_1_1_2"/><i><font color="Green">E79</font></i>: 
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="polyred.html#E3:75_2_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self">Def5</a>, <a class="ref" href="polynom7.html#D2">POLYNOM7:def 2</a></i>;<br/> <a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polyred.html#E5:75_2_1"><i><font color="Green">E66</font></i></a>, <a class="txt" href="polyred.html#E6:75_2_1_1_1_2_1_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="termord.html#D9">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">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K23">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="termord.html#T38">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">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K23">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polyred.html#E6:75_2_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_2_1_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="termord.html#T40">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">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K23">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K23">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p0">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p5">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T80">POLYNOM1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="termord.html#K5">HM</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K23">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T83">POLYNOM1:83</a></i>
<br/>.= 
<font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K25">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="polynom1.html#K15">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3">(<span class="default"><a href="termord.html#K4">HC</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom7.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="polyred.html#K1" target="_self">*'</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T82">POLYNOM1:82</a></i>
;<br/><a NAME="E22:75_2_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="polyred.html#R3" target="_self">reduces_to</a>  <a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E5:75_2_1"><i><font color="Green">E66</font></i></a>, <a class="txt" href="polyred.html#E9:75_2_1_1_1_2_1_1_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="polyred.html#E20:75_2_1_1_1_2_1_1_2"><i><font color="Green">E79</font></i></a>, <a class="ref" href="polyred.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E23:75_2_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="polyred.html#R4" target="_self">reduces_to</a>  <a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="polyred.html#D6" target="_self">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">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <span class="p3">(<span class="default"><a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #)
 <b>by </b><i><a class="txt" href="polyred.html#E1:75_2"><i><font color="Green">E63</font></i></a>, <a class="txt" href="polyred.html#E19:75_2_1_1_1_2_1_1_2"><i><font color="Green">E78</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">Red</a> <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="polyred.html#R1" target="_self">&lt;=</a>  <a href="termord.html#K6">Red</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="polyred.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E26:75_2_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="polyred.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E8:75_2_1"><i><font color="Green">E69</font></i></a>, <a class="txt" href="polyred.html#E1:75_2_1_1_1_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="polyred.html#E50"><i><font color="Green">Lemma43</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">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #)
 <b>by </b><i><a class="ref" href="polyred.html#D2" target="_self">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">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></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">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #)
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:75_2"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> st  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Olive">b<sub>1</sub></font> <a href="polyred.html#R4" target="_self">reduces_to</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #)
 ;<br/>


</div><b>end;</b></div>
<a NAME="E8:75"/><i><font color="Green">E63</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="polyred.html#E6:75"><i><font color="Green">E61</font></i></a>, <a class="txt" href="polyred.html#E7:75"><i><font color="Green">E62</font></i></a>);<br/></i>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:75"/><i><font color="Green">E64</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>
<a NAME="E11:75"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#K13">FinOrd</a> <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #)
 
<b>by </b><i><a class="txt" href="polyred.html#E1:75"><i><font color="Green">E58</font></i></a>, <a class="txt" href="polyred.html#E8:75"><i><font color="Green">E63</font></i></a>, <a class="txt" href="polyred.html#E10:75"><i><font color="Green">E64</font></i></a></i>;<br/>
<a NAME="E12:75"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="polyred.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="polyred.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E13:75"/>
<font color="Maroon">c<sub>6</sub></font> <a href="polyred.html#R2" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="polyred.html#E5:75"><i><font color="Green">E60</font></i></a>, <a class="ref" href="polyred.html#D3" target="_self">Def3</a></i>;<br/>


</div>
