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

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:5_1_2"/><i><font color="Green">E4</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>given </b><font color="Maroon">c<sub>4</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><a NAME="E2:5_1_2"/><i><font color="Green">E5</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E3:5_1_2"/><i><font color="Green">E6</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span> or  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 )
 <b>and </b><br/><a NAME="E4:5_1_2"/><i><font color="Green">E7</font></i>: 
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="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> holds <br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">c<sub>4</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="Olive">b<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E5:5_1_2"/><i><font color="Green">E8</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="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> 
 ;<br/>

<b>assume </b><a NAME="E6:5_1_2"/><i><font color="Green">E9</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>given </b><font color="Maroon">c<sub>5</sub></font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><a NAME="E7:5_1_2"/><i><font color="Green">E10</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E8:5_1_2"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span> or  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 )
 <b>and </b><br/><a NAME="E9:5_1_2"/><i><font color="Green">E12</font></i>: 
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="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> holds <br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">c<sub>5</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="Olive">b<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E10:5_1_2"/><i><font color="Green">E13</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="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>3</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> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> 
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>,   <a href="hidden.html#M1">set</a> ] means (  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font> );<br/>
<a NAME="E11:5_1_2"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[1,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1]
 
<b>by </b><i><a class="txt" href="uproots.html#E3:5_1_2"><i><font color="Green">E6</font></i></a>, <a class="txt" href="uproots.html#E8:5_1_2"><i><font color="Green">E11</font></i></a></i>;<br/>
<a NAME="E12:5_1_2"/><i><font color="Green">E15</font></i>: 
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>4</sub></font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="binop_2.html#K23">+</a> 1,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:5_1_2_1"/><i><font color="Green">E16</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E2:5_1_2_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E3:5_1_2_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>]
 <b>and </b><br/><a NAME="E4:5_1_2_1"/>
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>;<br/>
<b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span> = 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><a href="subset_1.html#K10">choose</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="uproots.html#E2:5_1_2"><i><font color="Green">E5</font></i></a>, <a class="txt" href="uproots.html#E4:5_1_2"><i><font color="Green">E7</font></i></a>, <a class="txt" href="uproots.html#E1:5_1_2_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="uproots.html#E2:5_1_2_1"><i><font color="Green">E17</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="uproots.html#E2:5_1_2"><i><font color="Green">E5</font></i></a>, <a class="txt" href="uproots.html#E9:5_1_2"><i><font color="Green">E12</font></i></a>, <a class="txt" href="uproots.html#E1:5_1_2_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="uproots.html#E2:5_1_2_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="uproots.html#E3:5_1_2_1"><i><font color="Green">E18</font></i></a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E13:5_1_2"/><i><font color="Green">E16</font></i>: 
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>4</sub></font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="uproots.html#S1" target="_self">UPROOTS:sch 1</a>(<a class="txt" href="uproots.html#E11:5_1_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="uproots.html#E12:5_1_2"><i><font color="Green">E15</font></i></a>);<br/></i>
<a NAME="E14:5_1_2"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_2_2"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:5_1_2_2_1"/>
(  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 or  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_2_2_1_1"><b>suppose </b></a><a NAME="E1:5_1_2_2_1_1"/><i><font color="Green">E18</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>4</sub></font> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="txt" href="uproots.html#E2:5_1_2"><i><font color="Green">E5</font></i></a>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="uproots.html#E7:5_1_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="uproots.html#E1:5_1_2_2_1_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_2_2_1_2"><b>suppose </b></a><a NAME="E1:5_1_2_2_1_2"/><i><font color="Green">E18</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_2_2_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:5_1_2_2_1_2_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/><a NAME="E2:5_1_2_2_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:5_1_2_2_1_2_1"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><b>hence </b><a NAME="E4:5_1_2_2_1_2_1"/>
<font color="Maroon">c<sub>4</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> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="uproots.html#E13:5_1_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="uproots.html#E1:5_1_2_2_1_2"><i><font color="Green">E18</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:5_1_2_2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="uproots.html#E2:5_1_2"><i><font color="Green">E5</font></i></a>, <a class="txt" href="uproots.html#E7:5_1_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_2_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:5_1_2_3"/><i><font color="Green">E18</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> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><a NAME="E2:5_1_2_3"/><i><font color="Green">E19</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="uproots.html#E1:5_1_2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="uproots.html#E6:5_1_2"><i><font color="Green">E9</font></i></a>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E3:5_1_2_3"/><i><font color="Green">E20</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="uproots.html#E1:5_1_2"><i><font color="Green">E4</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="txt" href="uproots.html#E5:5_1_2"><i><font color="Green">E8</font></i></a>, <a class="txt" href="uproots.html#E1:5_1_2_3"><i><font color="Green">E18</font></i></a></i>
<br/>.= 
<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="uproots.html#E10:5_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="uproots.html#E14:5_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="uproots.html#E1:5_1_2_3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="uproots.html#E2:5_1_2_3"><i><font color="Green">E19</font></i></a>, <a class="txt" href="uproots.html#E3:5_1_2_3"><i><font color="Green">E20</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E16:5_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="uproots.html#E1:5_1_2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="uproots.html#E6:5_1_2"><i><font color="Green">E9</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


</div>
