<?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  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> non <a href="realset2.html#V3">trivial</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:36"/><i><font color="Green">E26</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>



<a NAME="E2:36"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:36"/><i><font color="Green">E28</font></i>: 
 <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="polynom2.html#E1:36"><i><font color="Green">E26</font></i></a></i>;<br/>
<a NAME="E5:36"/><i><font color="Green">E29</font></i>: 
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#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:36_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:36_1"/><b>then </b><i><font color="Green">E30</font></i>: 
not <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="polynom2.html#E4:36"><i><font color="Green">E28</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D5">POLYNOM1:def 5</a></i>
<br/>.= 
0 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E2:36_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font>

;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="triang_1.html#K2">SgmX</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="triang_1.html#K2">SgmX</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E7:36"/><i><font color="Green">E30</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> &amp;  <a href="polynom2.html#K3" target="_self">eval</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_4.html#K3">Product</a> <font color="Maroon">c<sub>9</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> holds <br/><font color="Maroon">c<sub>9</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom2.html#K2" target="_self">*</a> <span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="ref" href="polynom2.html#D2" target="_self">Def2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E9:36"/><i><font color="Green">E31</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> &amp;  <a href="polynom2.html#K3" target="_self">eval</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_4.html#K3">Product</a> <font color="Maroon">c<sub>10</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font> holds <br/><font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom2.html#K2" target="_self">*</a> <span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="ref" href="polynom2.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E10:36"/><i><font color="Green">E32</font></i>: 
(  <a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font> <a href="orders_1.html#R3">linearly_orders</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font> <a href="orders_1.html#R3">linearly_orders</a>  <a href="polynom2.html#K1" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="polynom2.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E11:36"/><i><font color="Green">E33</font></i>: 
 <a href="polynom2.html#K1" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="polynom2.html#E4:36"><i><font color="Green">E28</font></i></a>, <a class="ref" href="polynom1.html#T42">POLYNOM1:42</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:36_2"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font> or  not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1"><b>suppose </b></a><a NAME="E1:36_2_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><a NAME="E2:36_2_1"/><i><font color="Green">E35</font></i>: 
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>  <a href="polynom2.html#K1" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:36_2_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_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="E1:36_2_1_1_1_1"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font> )
 </span><b>by </b><i><a class="txt" href="polynom2.html#E11:36"><i><font color="Green">E33</font></i></a>, <a class="txt" href="polynom2.html#E1:36_2_1_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_1_1_1_1"><b>case </b></a><a NAME="E1:36_2_1_1_1_1_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:36_2_1_1_1_1_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E1:36_2_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_1_1_1_2"><b>case </b></a><a NAME="E1:36_2_1_1_1_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:36_2_1_1_1_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:36_2_1_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>


</div><b>end;</b></div><a NAME="E3:36_2_1"/><i><font color="Green">E36</font></i>: 
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>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:36_2_1_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_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="E1:36_2_1_2_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_2_1_1_1"><b>case </b></a><a NAME="E1:36_2_1_2_1_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><div class="add"><a NAME="E2:36_2_1_2_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></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/><b>hence </b><a NAME="E3:36_2_1_2_1_1_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom2.html#E11:36"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_1_2_1_1_2"><b>case </b></a><a NAME="E1:36_2_1_2_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><div class="add"><a NAME="E2:36_2_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E5:36"><i><font color="Green">E29</font></i></a></i>;<br/><a NAME="E3:36_2_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="polynom2.html#E1:36_2_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>;<br/><b>hence </b><a NAME="E4:36_2_1_2_1_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:36_2_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>


</div><b>end;</b></div><a NAME="E4:36_2_1"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="polynom2.html#K1" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E2:36_2_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><a NAME="E5:36_2_1"/><i><font color="Green">E38</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E7:36"><i><font color="Green">E30</font></i></a>, <a class="txt" href="polynom2.html#E9:36"><i><font color="Green">E31</font></i></a>, <a class="txt" href="polynom2.html#E2:36_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="polynom2.html#E3:36_2_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><a NAME="E6:36_2_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom2.html#E10:36"><i><font color="Green">E32</font></i></a>, <a class="txt" href="polynom2.html#E1:36_2_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="triang_1.html#D2">TRIANG_1:def 2</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E8:36_2_1"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:36_2_1"/><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E12:36_2_1"/><i><font color="Green">E41</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/><i><font color="Green">E42</font></i>: <font color="Maroon">c<sub>12</sub></font> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E10:36_2_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E2:36_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="polynom2.html#E3:36_2_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>
<br/>.= 
<font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="polynom2.html#E12:36_2_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
;<br/><a NAME="E14:36_2_1"/><i><font color="Green">E43</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font> )
 <b>by </b><i><a class="txt" href="polynom2.html#E8:36_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom2.html#E10:36_2_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E16:36_2_1"/><i><font color="Green">E44</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/><a NAME="E17:36_2_1"/><i><font color="Green">E45</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E16:36_2_1"><i><font color="Green">E44</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E18:36_2_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E9:36"><i><font color="Green">E31</font></i></a>, <a class="txt" href="polynom2.html#E10:36_2_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E19:36_2_1"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E8:36_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom2.html#E10:36_2_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E20:36_2_1"/><i><font color="Green">E48</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E7:36"><i><font color="Green">E30</font></i></a>, <a class="txt" href="polynom2.html#E12:36_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="polynom2.html#E13:36_2_1"><i><font color="Green">E42</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E21:36_2_1"/><i><font color="Green">E49</font></i>: 
 <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="polynom1.html#T41">POLYNOM1:41</a></i>;<br/><a NAME="E22:36_2_1"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom2.html#E1:36_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="polynom2.html#E8:36_2_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/><a NAME="E23:36_2_1"/><i><font color="Green">E51</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E24:36_2_1"/>
 <a href="polynom2.html#K1" target="_self">support</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T41">POLYNOM1:41</a></i>;<br/><a NAME="E25:36_2_1"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom2.html#E1:36_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="polynom2.html#E4:36_2_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="polynom2.html#E8:36_2_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/><b>then </b><i><font color="Green">E53</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="polynom2.html#E8:36_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom2.html#E25:36_2_1"><i><font color="Green">E52</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
;<br/><i><font color="Green">E54</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="polynom2.html#E22:36_2_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="polynom2.html#E8:36_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom2.html#E22:36_2_1"><i><font color="Green">E50</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
;<br/><i><font color="Green">E55</font></i>: <font color="Maroon">c<sub>9</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom2.html#K2" target="_self">*</a> <span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E7:36"><i><font color="Green">E30</font></i></a>, <a class="txt" href="polynom2.html#E4:36_2_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="polynom2.html#E14:36_2_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="polynom2.html#E20:36_2_1"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E26:36_2_1"><i><font color="Green">E53</font></i></a>, <a class="ref" href="polynom1.html#D5">POLYNOM1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p4">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p5">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p5">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p4">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p5">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p5">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom2.html#K2" target="_self">*</a> <span class="p4">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p5">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p5">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E27:36_2_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="polynom2.html#T2" target="_self">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p4">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p5">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p5">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E9:36"><i><font color="Green">E31</font></i></a>, <a class="txt" href="polynom2.html#E14:36_2_1"><i><font color="Green">E43</font></i></a>, <a class="txt" href="polynom2.html#E18:36_2_1"><i><font color="Green">E46</font></i></a></i>
;<br/><a NAME="E29:36_2_1"/><i><font color="Green">E56</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> holds <br/><font color="Maroon">c<sub>9</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_7"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>15</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:36_2_1_7"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>11</sub></font> )
 ;<br/>

<a NAME="E2:36_2_1_7"/><b>then </b><i><font color="Green">E58</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="polynom2.html#E16:36_2_1"><i><font color="Green">E44</font></i></a>, <a class="txt" href="polynom2.html#E17:36_2_1"><i><font color="Green">E45</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E3:36_2_1_7"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="polynom2.html#E13:36_2_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="polynom2.html#E18:36_2_1"><i><font color="Green">E46</font></i></a>, <a class="txt" href="polynom2.html#E1:36_2_1_7"><i><font color="Green">E57</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E4:36_2_1_7"/><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2_1_7_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:36_2_1_7_1"/>
<span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:36_2_1_7_1"/><b>then </b><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="polynom2.html#E12:36_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="polynom2.html#E3:36_2_1_7"><i><font color="Green">E59</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E3:36_2_1_7_1"/><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="polynom2.html#E2:36_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="polynom2.html#E3:36_2_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="polynom2.html#E8:36_2_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<a NAME="E4:36_2_1_7_1"/>
 <a href="triang_1.html#K2">SgmX</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="polynom2.html#E10:36"><i><font color="Green">E32</font></i></a>, <a class="ref" href="triang_1.html#T8">TRIANG_1:8</a></i>;<br/>
<b>hence </b><a NAME="E5:36_2_1_7_1"/>
contradiction
 <b>by </b><i><a class="txt" href="polynom2.html#E8:36_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom2.html#E10:36_2_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="polynom2.html#E12:36_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="polynom2.html#E13:36_2_1"><i><font color="Green">E42</font></i></a>, <a class="txt" href="polynom2.html#E1:36_2_1_7"><i><font color="Green">E57</font></i></a>, <a class="txt" href="polynom2.html#E3:36_2_1_7"><i><font color="Green">E59</font></i></a>, <a class="txt" href="polynom2.html#E2:36_2_1_7_1"><i><font color="Green">E61</font></i></a>, <a class="txt" href="polynom2.html#E3:36_2_1_7_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:36_2_1_7"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="polynom2.html#E10:36"><i><font color="Green">E32</font></i></a>, <a class="txt" href="polynom2.html#E4:36_2_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="polynom2.html#E21:36_2_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="triang_1.html#D2">TRIANG_1:def 2</a></i>;<br/>
<a NAME="E6:36_2_1_7"/><b>then </b><i><font color="Green">E61</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E7:36_2_1_7"/>
<span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="polynom2.html#E12:36_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="polynom2.html#E3:36_2_1_7"><i><font color="Green">E59</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E8:36_2_1_7"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="polynom2.html#E12:36_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="polynom2.html#E23:36_2_1"><i><font color="Green">E51</font></i></a>, <a class="txt" href="polynom2.html#E3:36_2_1_7"><i><font color="Green">E59</font></i></a>, <a class="txt" href="polynom2.html#E6:36_2_1_7"><i><font color="Green">E61</font></i></a>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/>
<b>then </b><i><font color="Green">E63</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E8:36_2_1_7"><i><font color="Green">E62</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E12:36_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="polynom2.html#E3:36_2_1_7"><i><font color="Green">E59</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/>
<a NAME="E10:36_2_1_7"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="polynom2.html#E9:36"><i><font color="Green">E31</font></i></a>, <a class="txt" href="polynom2.html#E16:36_2_1"><i><font color="Green">E44</font></i></a>, <a class="txt" href="polynom2.html#E17:36_2_1"><i><font color="Green">E45</font></i></a>, <a class="txt" href="polynom2.html#E1:36_2_1_7"><i><font color="Green">E57</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E11:36_2_1_7"/><i><font color="Green">E65</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="polynom2.html#E10:36"><i><font color="Green">E32</font></i></a>, <a class="txt" href="polynom2.html#E21:36_2_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="triang_1.html#D2">TRIANG_1:def 2</a></i>;<br/>
<a NAME="E12:36_2_1_7"/>
<span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="polynom2.html#E10:36_2_1_7"><i><font color="Green">E64</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E13:36_2_1_7"/><b>then </b><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="polynom2.html#E10:36_2_1_7"><i><font color="Green">E64</font></i></a>, <a class="txt" href="polynom2.html#E11:36_2_1_7"><i><font color="Green">E65</font></i></a>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/>
<b>then </b><i><font color="Green">E67</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom2.html#K2" target="_self">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E13:36_2_1_7"><i><font color="Green">E66</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E10:36_2_1_7"><i><font color="Green">E64</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/>
<b>thus </b><font color="Maroon">c<sub>9</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font> = 
<span class="p1">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E7:36"><i><font color="Green">E30</font></i></a>, <a class="txt" href="polynom2.html#E5:36_2_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="polynom2.html#E2:36_2_1_7"><i><font color="Green">E58</font></i></a>, <a class="txt" href="polynom2.html#E9:36_2_1_7"><i><font color="Green">E63</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p4">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p4">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E5:36"><i><font color="Green">E29</font></i></a>, <a class="txt" href="polynom2.html#E4:36_2_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="polynom2.html#E4:36_2_1_7"><i><font color="Green">E60</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>15</sub></font>
<b>by </b><i><a class="txt" href="polynom2.html#E9:36"><i><font color="Green">E31</font></i></a>, <a class="txt" href="polynom2.html#E2:36_2_1_7"><i><font color="Green">E58</font></i></a>, <a class="txt" href="polynom2.html#E14:36_2_1_7"><i><font color="Green">E67</font></i></a></i>
;<br/>


</div><b>end;</b></div><a NAME="E30:36_2_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E4:36"><i><font color="Green">E28</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E31:36_2_1"/>
 <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="polynom1.html#T41">POLYNOM1:41</a></i>;<br/><a NAME="E32:36_2_1"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E30:36_2_1"><i><font color="Green">E57</font></i></a></i>;<br/><a NAME="E33:36_2_1"/><i><font color="Green">E59</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E34:36_2_1"/><b>then </b><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E2:36"><i><font color="Green">E27</font></i></a>, <a class="txt" href="polynom2.html#E32:36_2_1"><i><font color="Green">E58</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><a NAME="E35:36_2_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="polynom2.html#E34:36_2_1"><i><font color="Green">E60</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>16</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E38:36_2_1"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>15</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 ;<br/><a NAME="E39:36_2_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom2.html#E2:36"><i><font color="Green">E27</font></i></a>, <a class="txt" href="polynom2.html#E8:36_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom2.html#E32:36_2_1"><i><font color="Green">E58</font></i></a>, <a class="txt" href="polynom2.html#E33:36_2_1"><i><font color="Green">E59</font></i></a>, <a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/><a NAME="E40:36_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <span class="p3">(<span class="default"><a href="yellow_1.html#K1">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/><a NAME="E41:36_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom2.html#E8:36_2_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom2.html#E28:36_2_1"><i><font color="Green">E55</font></i></a>, <a class="txt" href="polynom2.html#E38:36_2_1"><i><font color="Green">E61</font></i></a>, <a class="txt" href="polynom2.html#E39:36_2_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><b>hence </b> <a href="polynom2.html#K3" target="_self">eval</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>16</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_4.html#K3">Product</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E7:36"><i><font color="Green">E30</font></i></a>, <a class="txt" href="polynom2.html#E5:36_2_1"><i><font color="Green">E38</font></i></a>, <a class="txt" href="polynom2.html#E19:36_2_1"><i><font color="Green">E47</font></i></a>, <a class="txt" href="polynom2.html#E29:36_2_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="polynom2.html#T8" target="_self">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom2.html#K3" target="_self">eval</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="polynom2.html#K3" target="_self">eval</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E4:36"><i><font color="Green">E28</font></i></a>, <a class="txt" href="polynom2.html#E9:36"><i><font color="Green">E31</font></i></a>, <a class="txt" href="polynom2.html#E38:36_2_1"><i><font color="Green">E61</font></i></a>, <a class="ref" href="polynom2.html#T17" target="_self">Th17</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_2_2"><b>suppose </b></a><a NAME="E1:36_2_2"/><i><font color="Green">E34</font></i>: 
not <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><i><font color="Green">E35</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D5">POLYNOM1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 0
<b>by </b><i><a class="txt" href="polynom2.html#E1:36_2_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="polynom1.html#D7">POLYNOM1:def 7</a></i>
;<br/><a NAME="E3:36_2_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E4:36"><i><font color="Green">E28</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:36_2_2"/>
 <a href="polynom2.html#K1" target="_self">support</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="polynom1.html#T41">POLYNOM1:41</a></i>;<br/><a NAME="E5:36_2_2"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E3:36_2_2"><i><font color="Green">E36</font></i></a></i>;<br/><a NAME="E6:36_2_2"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E7:36_2_2"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="polynom2.html#E2:36"><i><font color="Green">E27</font></i></a>, <a class="txt" href="polynom2.html#E5:36_2_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><a NAME="E8:36_2_2"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="polynom2.html#E7:36_2_2"><i><font color="Green">E38</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E11:36_2_2"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 ;<br/><b>thus </b> <a href="polynom2.html#K3" target="_self">eval</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>12</sub></font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="polynom2.html#K3" target="_self">eval</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E5:36"><i><font color="Green">E29</font></i></a>, <a class="txt" href="polynom2.html#E11:36"><i><font color="Green">E33</font></i></a>, <a class="txt" href="polynom2.html#E1:36_2_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="polynom2.html#E11:36_2_2"><i><font color="Green">E39</font></i></a>, <a class="txt" href="polynom2.html#E27"><i><font color="Green">Lemma24</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom2.html#K3" target="_self">eval</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="polynom2.html#K3" target="_self">eval</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom2.html#E4:36"><i><font color="Green">E28</font></i></a>, <a class="txt" href="polynom2.html#E2:36_2_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="polynom2.html#E11:36_2_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="polynom2.html#T17" target="_self">Th17</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
