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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></font> being  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default">2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> </span>)</span><b> such that </b><br/><a NAME="E2:23"/><i><font color="Green">E14</font></i>: 
 <a href="polynom3.html#K6" target="_self">Decomp</a> <font color="Maroon">c<sub>1</sub></font>,2 <a href="hidden.html#R1">=</a>  <a href="triang_1.html#K2">SgmX</a> <span class="p1">(<span class="default"><a href="polynom3.html#K5" target="_self">TuplesOrder</a> 2</span>)</span>,<font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E3:23"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_2.html#M2">Element</a> of 2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> iff  <a href="wsierp_1.html#K8">Sum</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="polynom3.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E4:23"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:23_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:23_1_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="finseq_2.html#M2">Element</a> of 2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  ;<br/>
<b>consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:23_1_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T120">FINSEQ_2:120</a></i>;<br/>
<i><font color="Green">E19</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="wsierp_1.html#K8">Sum</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="polynom3.html#E4:23_1_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="rvsum_1.html#T107">RVSUM_1:107</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="polynom3.html#E3:23"><i><font color="Green">E15</font></i></a>, <a class="txt" href="polynom3.html#E1:23_1_1"><i><font color="Green">E17</font></i></a></i>
;<br/>
<a NAME="E6:23_1_1"/><b>then </b><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E7:23_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E8:23_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="polynom3.html#E5:23_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<b>hence </b><a NAME="E9:23_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="polynom3.html#E4:23_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="polynom3.html#E6:23_1_1"><i><font color="Green">E20</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:23_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:23_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
 <b>and </b><br/><a NAME="E5:23_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>
<a NAME="E6:23_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="polynom3.html#E5:23_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
 <a href="wsierp_1.html#K8">Sum</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> = 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#T107">RVSUM_1:107</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E6:23_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>

;<br/>
<b>hence </b><a NAME="E8:23_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="polynom3.html#E3:23"><i><font color="Green">E15</font></i></a>, <a class="txt" href="polynom3.html#E4:23_1"><i><font color="Green">E17</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>   <a href="finseq_2.html#M2">Element</a> of 2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  = <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Maroon">a<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E6:23"/><i><font color="Green">E17</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E7:23"/><i><font color="Green">E18</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#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="finseq_1.html#S2">FINSEQ_1:sch 2</a>();<br/></i>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span>;<br/>
<a NAME="E8:23"/><i><font color="Green">E19</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T42">FINSEQ_1:42</a></i>;<br/>
<a NAME="E9:23"/><i><font color="Green">E20</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="polynom3.html#E6:23"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_2.html#T19">FINSEQ_2:19</a></i>;<br/>
<a NAME="E10:23"/><b>then </b><i><font color="Green">E21</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E11:23"/><i><font color="Green">E22</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="polynom3.html#E6:23"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E12:23"/><i><font color="Green">E23</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:23_2"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:23_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:23_2_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 <b>and </b><br/><a NAME="E4:23_2_1"/><i><font color="Green">E25</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/>
<a NAME="E5:23_2_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</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"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="polynom3.html#E10:23"><i><font color="Green">E21</font></i></a>, <a class="txt" href="polynom3.html#E3:23_2_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="finseq_1.html#T11">FINSEQ_1:11</a></i>;<br/>
<a NAME="E6:23_2_1"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>6</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"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_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="E1:23_2_1_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 </span><b>by </b><i><a class="txt" href="polynom3.html#E6:23_2_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:23_2_1_1_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:23_2_1_1_1_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom3.html#E7:23"><i><font color="Green">E18</font></i></a></i>;<br/><a NAME="E3:23_2_1_1_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="polynom3.html#E1:23_2_1_1_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E4:23_2_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="polynom3.html#E11:23"><i><font color="Green">E22</font></i></a>, <a class="txt" href="polynom3.html#E1:23_2_1_1_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><b>hence </b><a NAME="E5:23_2_1_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="polynom3.html#E4:23_2_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="polynom3.html#E2:23_2_1_1_1_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="polynom3.html#E3:23_2_1_1_1_1"><i><font color="Green">E29</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:23_2_1_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/><div class="add"><b>then </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom3.html#E6:23"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
<br/>.= 
<span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 0</span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i><a class="ref" href="jordan3.html#T2">JORDAN3:2</a></i>
;<br/><b>hence </b><a NAME="E3:23_2_1_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="polynom3.html#E4:23_2_1"><i><font color="Green">E25</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:23_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 ;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:23_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E4:23_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
 <b>and </b><br/><a NAME="E5:23_2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>
<a NAME="E6:23_2"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 
;<br/>
<a NAME="E7:23_2"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:23_2_2_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> )
 </span><b>by </b><i><a class="txt" href="polynom3.html#E5:23_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="polynom3.html#E7:23_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_2_1_1"><b>suppose </b></a><a NAME="E1:23_2_2_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:23_2_2_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E10:23"><i><font color="Green">E21</font></i></a>, <a class="ref" href="finseq_1.html#T6">FINSEQ_1:6</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom3.html#E6:23"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="polynom3.html#E4:23_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="polynom3.html#E1:23_2_2_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="jordan3.html#T2">JORDAN3:2</a></i>
;<br/><b>hence </b><a NAME="E4:23_2_2_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E2:23_2_2_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_2_2_1_2"><b>suppose </b></a><a NAME="E1:23_2_2_1_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:23_2_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="polynom3.html#E7:23"><i><font color="Green">E18</font></i></a>, <a class="txt" href="polynom3.html#E4:23_2"><i><font color="Green">E24</font></i></a></i>;<br/><a NAME="E3:23_2_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="polynom3.html#E11:23"><i><font color="Green">E22</font></i></a>, <a class="txt" href="polynom3.html#E1:23_2_2_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>hence </b><a NAME="E4:23_2_2_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E8:23"><i><font color="Green">E19</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E9:23_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:23_3"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 <b>and </b><br/><a NAME="E2:23_3"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>
 <b>and </b><br/><a NAME="E3:23_3"/><i><font color="Green">E26</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="polynom3.html#E1:23_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="polynom3.html#E2:23_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="finseq_3.html#T25">FINSEQ_3:25</a></i>;<br/><a NAME="E5:23_3"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</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"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</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"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="txt" href="polynom3.html#E10:23"><i><font color="Green">E21</font></i></a>, <a class="txt" href="polynom3.html#E1:23_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="polynom3.html#E2:23_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="finseq_1.html#T11">FINSEQ_1:11</a></i>;<br/><a NAME="E6:23_3"/><b>then </b><i><font color="Green">E27</font></i>: 
( ( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>5</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"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span> ) &amp; ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>6</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"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="tarski.html#K1">}</a></span> ) )
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:23_3_1_1"/>
( ( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> ) or ( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 ) or ( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> ) or ( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 ) )
 </span><b>by </b><i><a class="txt" href="polynom3.html#E6:23_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_3_1_1_1"><b>suppose </b></a><a NAME="E1:23_3_1_1_1"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/><div class="add"><a NAME="E2:23_3_1_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="polynom3.html#E11:23"><i><font color="Green">E22</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>;<br/><a NAME="E3:23_3_1_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> )
 <b>by </b><i><a class="txt" href="polynom3.html#E7:23"><i><font color="Green">E18</font></i></a>, <a class="txt" href="polynom3.html#E1:23_3_1_1_1"><i><font color="Green">E28</font></i></a></i>;<br/><b>hence </b><a NAME="E4:23_3_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="polynom3.html#E3:23_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polynom3.html#E2:23_3_1_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="group_7.html#T2">GROUP_7:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_3_1_1_2"><b>suppose </b></a><a NAME="E1:23_3_1_1_2"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div class="add"><b>then </b><i><font color="Green">E29</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="polynom3.html#E11:23"><i><font color="Green">E22</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom3.html#E7:23"><i><font color="Green">E18</font></i></a>, <a class="txt" href="polynom3.html#E1:23_3_1_1_2"><i><font color="Green">E28</font></i></a></i>
;<br/><a NAME="E3:23_3_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom3.html#E6:23"><i><font color="Green">E17</font></i></a>, <a class="txt" href="polynom3.html#E1:23_3_1_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>;<br/><a NAME="E4:23_3_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="polynom3.html#E3:23_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polynom3.html#E2:23_3_1_1_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="group_7.html#T2">GROUP_7:2</a></i>;<br/><b>hence </b><a NAME="E5:23_3_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="polynom3.html#E1:23_3_1_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_3_1_1_3"><b>suppose </b></a><a NAME="E1:23_3_1_1_3"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/><div class="add"><b>then </b><i><font color="Green">E29</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="polynom3.html#E11:23"><i><font color="Green">E22</font></i></a>, <a class="ref" href="finseq_1.html#D7">FINSEQ_1:def 7</a></i>
<br/>.= 
<span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom3.html#E7:23"><i><font color="Green">E18</font></i></a>, <a class="txt" href="polynom3.html#E1:23_3_1_1_3"><i><font color="Green">E28</font></i></a></i>
;<br/><a NAME="E3:23_3_1_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p3"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom3.html#E6:23"><i><font color="Green">E17</font></i></a>, <a class="txt" href="polynom3.html#E1:23_3_1_1_3"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_1.html#T59">FINSEQ_1:59</a></i>;<br/><a NAME="E4:23_3_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="polynom3.html#E3:23_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polynom3.html#E2:23_3_1_1_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="group_7.html#T2">GROUP_7:2</a></i>;<br/><b>hence </b><a NAME="E5:23_3_1_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="polynom3.html#E1:23_3_1_1_3"><i><font color="Green">E28</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="23_3_1_1_4"><b>suppose </b></a><a NAME="E1:23_3_1_1_4"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:23_3_1_1_4"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E8:23_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/></div><b>end;</b></div>
<a NAME="E14:23"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<a NAME="E15:23"/><b>then </b><i><font color="Green">E24</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_1.html#K7">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>1</sub></font></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="polynom3.html#E9:23"><i><font color="Green">E20</font></i></a>, <a class="ref" href="finseq_4.html#T77">FINSEQ_4:77</a></i>;<br/>
<a NAME="E16:23"/>
 <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="polynom3.html#K5" target="_self">TuplesOrder</a> 2</span>)</span> <a href="hidden.html#R1">=</a> 2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="orders_1.html#T100">ORDERS_1:100</a></i>;<br/>
<a NAME="E17:23"/><b>then </b>
 <a href="polynom3.html#K5" target="_self">TuplesOrder</a> 2 <a href="orders_1.html#R3">linearly_orders</a> 2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="orders_1.html#T133">ORDERS_1:133</a></i>;<br/>
<a NAME="E18:23"/><b>then </b>
 <a href="polynom3.html#K5" target="_self">TuplesOrder</a> 2 <a href="orders_1.html#R3">linearly_orders</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="orders_1.html#T134">ORDERS_1:134</a></i>;<br/>
<b>hence </b><a NAME="E19:23"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <font color="Maroon">c<sub>1</sub></font>,2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="polynom3.html#E2:23"><i><font color="Green">E14</font></i></a>, <a class="txt" href="polynom3.html#E4:23"><i><font color="Green">E16</font></i></a>, <a class="txt" href="polynom3.html#E12:23"><i><font color="Green">E23</font></i></a>, <a class="txt" href="polynom3.html#E15:23"><i><font color="Green">E24</font></i></a>, <a class="ref" href="triang_1.html#T9">TRIANG_1:9</a></i>;<br/>


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