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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="afinsq_1.html#NM2">XFinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:25"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 is   <a href="nat_1.html#NM1">Nat</a> &amp;  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:25"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="ref" href="prgcor_2.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E3:25"/><i><font color="Green">E19</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="prgcor_2.html#T2" target="_self">Th2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 as   <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="rvsum_1.html#K3">+</a> <font color="Maroon">c<sub>5</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  ;<br/>
<a NAME="E8:25"/><i><font color="Green">E20</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25"><i><font color="Green">E18</font></i></a>, <a class="ref" href="prgcor_2.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E9:25"/><i><font color="Green">E21</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25"><i><font color="Green">E18</font></i></a>, <a class="ref" href="prgcor_2.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E10:25"/><b>then </b><i><font color="Green">E22</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E8:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="euclid_2.html#T6">EUCLID_2:6</a></i>;<br/>
<a NAME="E11:25"/><b>then </b>
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E8:25"><i><font color="Green">E20</font></i></a>, <a class="txt" href="prgcor_2.html#E9:25"><i><font color="Green">E21</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E12:25"/><b>then </b>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E13:25"/><b>then </b>
 <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>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E14:25"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E8:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="afinsq_1.html#NM2">XFinSequence</a> of  <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E16:25"/><i><font color="Green">E24</font></i>: 
(  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="prgcor_2.html#R1" target="_self">is_an_xrep_of</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E14:25"><i><font color="Green">E23</font></i></a>, <a class="ref" href="prgcor_2.html#T7" target="_self">Th7</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span>;<br/>
<a NAME="E17:25"/><i><font color="Green">E25</font></i>: 
 <a href="afinsq_1.html#K1">len</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="afinsq_1.html#K1">len</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="afinsq_1.html#T48">AFINSQ_1:48</a></i>;<br/>
<a NAME="E18:25"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <span class="p1">(<span class="default"><a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span></span>)</span> <a href="prgcor_2.html#K6" target="_self">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies for <font color="Olive">b<sub>2</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>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><span class="p1">(<span class="default"><a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span></span>)</span> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 as   <a href="int_1.html#NM1">Integer</a> <b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a></i>;<br/>
<a NAME="E2:25_1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies 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> <font color="Maroon">c<sub>4</sub></font> holds <br/><span class="p1">(<span class="default"><a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span></span>)</span> <a href="prgcor_2.html#K6" target="_self">.</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>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:25_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><b>thus </b><a NAME="E2:25_1_1_1"/>
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> <font color="Maroon">c<sub>4</sub></font> holds <br/><span class="p1">(<span class="default"><a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span></span>)</span> <a href="prgcor_2.html#K6" target="_self">.</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>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:25_1_1_1_1"/><i><font color="Green">E27</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>4</sub></font> )
 ;<br/>

<a NAME="E2:25_1_1_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E14:25"><i><font color="Green">E23</font></i></a>, <a class="txt" href="prgcor_2.html#E16:25"><i><font color="Green">E24</font></i></a>, <a class="ref" href="prgcor_2.html#D5" target="_self">Def5</a>, <a class="txt" href="prgcor_2.html#E1:25_1_1_1_1"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E3:25_1_1_1_1"/>
<font color="Maroon">c<sub>11</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>7</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E9:25"><i><font color="Green">E21</font></i></a>, <a class="txt" href="prgcor_2.html#E10:25"><i><font color="Green">E22</font></i></a>, <a class="txt" href="prgcor_2.html#E1:25_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="E4:25_1_1_1_1"/><b>then </b><i><font color="Green">E29</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>7</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:25_1_1_1_1"/><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25"><i><font color="Green">E18</font></i></a>, <a class="ref" href="prgcor_2.html#D4" target="_self">Def4</a>, <a class="txt" href="prgcor_2.html#E1:25_1_1_1_1"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E6:25_1_1_1_1"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25"><i><font color="Green">E18</font></i></a>, <a class="ref" href="prgcor_2.html#D4" target="_self">Def4</a>, <a class="txt" href="prgcor_2.html#E1:25_1_1_1_1"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E7:25_1_1_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E5:25_1_1_1_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="prgcor_2.html#E6:25_1_1_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_1_1_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="rvsum_1.html#T26">RVSUM_1:26</a></i>;<br/>
<b>hence </b><a NAME="E8:25_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span></span>)</span> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="prgcor_2.html#E1:25_1_1_1_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25_1_1_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="afinsq_1.html#T48">AFINSQ_1:48</a></i>;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:25_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies 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> <font color="Maroon">c<sub>4</sub></font> holds <br/><span class="p1">(<span class="default"><a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span></span>)</span> <a href="prgcor_2.html#K6" target="_self">.</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>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> )
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:25_1"/>
<span class="p1">(<span class="default"><a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span></span>)</span> <a href="prgcor_2.html#K6" target="_self">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E16:25"><i><font color="Green">E24</font></i></a>, <a class="ref" href="afinsq_1.html#T48">AFINSQ_1:48</a></i>;<br/>
<b>hence </b><a NAME="E4:25_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <span class="p1">(<span class="default"><a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span></span>)</span> <a href="prgcor_2.html#K6" target="_self">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies for <font color="Olive">b<sub>2</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>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><span class="p1">(<span class="default"><a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span></span>)</span> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="prgcor_2.html#E2:25_1"><i><font color="Green">E26</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E19:25"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="prgcor_2.html#R4" target="_self">vector_add_prg</a>  <a href="afinsq_1.html#K11">Replace</a> <font color="Maroon">c<sub>8</sub></font>,0,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0</span>)</span>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E16:25"><i><font color="Green">E24</font></i></a>, <a class="txt" href="prgcor_2.html#E17:25"><i><font color="Green">E25</font></i></a>, <a class="ref" href="prgcor_2.html#D10" target="_self">Def10</a></i>;<br/>
<b>hence </b><a NAME="E20:25"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="afinsq_1.html#NM2">XFinSequence</a> of  <a href="numbers.html#K1">REAL</a>  st <font color="Maroon">c<sub>3</sub></font> <a href="prgcor_2.html#R4" target="_self">vector_add_prg</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>thus </b><a NAME="E21:25"/>
for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a> <a href="afinsq_1.html#NM2">XFinSequence</a> of  <a href="numbers.html#K1">REAL</a>  st <font color="Maroon">c<sub>3</sub></font> <a href="prgcor_2.html#R4" target="_self">vector_add_prg</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> holds <br/> <a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="afinsq_1.html#NM2">XFinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:25_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="prgcor_2.html#R4" target="_self">vector_add_prg</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:25_2"/><b>then </b><i><font color="Green">E27</font></i>: 
(  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; ex <font color="Olive">b<sub>1</sub></font> being  <a href="int_1.html#NM1">Integer</a> st <br/>( <font color="Maroon">c<sub>10</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies for <font color="Olive">b<sub>2</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>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>10</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span> ) ) )
 
<b>by </b><i><a class="ref" href="prgcor_2.html#D10" target="_self">Def10</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E4:25_2"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 &amp; ( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies 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> <font color="Maroon">c<sub>11</sub></font> holds <br/><font color="Maroon">c<sub>10</sub></font> <a href="prgcor_2.html#K6" target="_self">.</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>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="ref" href="prgcor_2.html#D10" target="_self">Def10</a>, <a class="txt" href="prgcor_2.html#E1:25_2"><i><font color="Green">E26</font></i></a></i>;<br/>
<a NAME="E5:25_2"/><i><font color="Green">E29</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25"><i><font color="Green">E18</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="prgcor_2.html#D4" target="_self">Def4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:25_2_1_1"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>11</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="25_2_1_1_1"><b>case </b></a><a NAME="E1:25_2_1_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:25_2_1_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i><a class="txt" href="prgcor_2.html#E3:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="prgcor_2.html#T5" target="_self">Th5</a></i>;<br/><a NAME="E3:25_2_1_1_1"/>
 <a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i><a class="txt" href="prgcor_2.html#E3:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="prgcor_2.html#E1:25_2_1_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="prgcor_2.html#T5" target="_self">Th5</a></i>;<br/><b>hence </b><a NAME="E4:25_2_1_1_1"/>
 <a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="prgcor_2.html#E2:25_2_1_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="rvsum_1.html#T28">RVSUM_1:28</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_2_1_1_2"><b>case </b></a><a NAME="E1:25_2_1_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font>;<br/><a NAME="E2:25_2_1_1_2"/>
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> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:25_2_1_1_2_1"/><i><font color="Green">E30</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> )
 ;<br/>

<a NAME="E2:25_2_1_1_2_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> 0 <a href="hidden.html#R2">in</a>  <a href="afinsq_1.html#K1">len</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="prgcor_2.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E3:25_2_1_1_2_1"/><b>then </b><i><font color="Green">E32</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</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> <font color="Maroon">c<sub>11</sub></font> holds <br/><span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="seq_1.html#K2">.</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="prgcor_2.html#K6" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="prgcor_2.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E4:25_2_1_1_2_1"/><i><font color="Green">E33</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E2:25_2_1_1_2_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="prgcor_2.html#E1:25_2_1_1_2_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="prgcor_2.html#D4" target="_self">Def4</a></i>;<br/>
<i><font color="Green">E34</font></i>: <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> = 
<font color="Maroon">c<sub>10</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>13</sub></font>
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25_2_1_1_2_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="prgcor_2.html#E3:25_2_1_1_2_1"><i><font color="Green">E32</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>13</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="prgcor_2.html#E4:25_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_2_1_1_2_1"><i><font color="Green">E33</font></i></a></i>
;<br/>
<a NAME="E6:25_2_1_1_2_1"/>
<font color="Maroon">c<sub>13</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>7</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E14:25"><i><font color="Green">E23</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_2_1_1_2_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E7:25_2_1_1_2_1"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E8:25_2_1_1_2_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25"><i><font color="Green">E18</font></i></a>, <a class="ref" href="prgcor_2.html#D4" target="_self">Def4</a>, <a class="txt" href="prgcor_2.html#E4:25_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_2_1_1_2_1"><i><font color="Green">E33</font></i></a></i>;<br/>
<a NAME="E9:25_2_1_1_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="prgcor_2.html#K6" target="_self">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="prgcor_2.html#E2:25"><i><font color="Green">E18</font></i></a>, <a class="ref" href="prgcor_2.html#D4" target="_self">Def4</a>, <a class="txt" href="prgcor_2.html#E4:25_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_2_1_1_2_1"><i><font color="Green">E33</font></i></a></i>;<br/>
<b>hence </b><a NAME="E10:25_2_1_1_2_1"/>
<span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="prgcor_2.html#E5:25_2_1_1_2_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="prgcor_2.html#E7:25_2_1_1_2_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="prgcor_2.html#E8:25_2_1_1_2_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="rvsum_1.html#T26">RVSUM_1:26</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:25_2_1_1_2"/>
 <a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a>, <a class="txt" href="prgcor_2.html#E14:25"><i><font color="Green">E23</font></i></a>, <a class="txt" href="prgcor_2.html#E4:25_2"><i><font color="Green">E28</font></i></a>, <a class="txt" href="prgcor_2.html#E5:25_2"><i><font color="Green">E29</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="E7:25_2"/>
 <a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rvsum_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" target="_self">XFS2FS*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>


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


</div>
