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

<a NAME="E1:1_1"/><i><font color="Green">E2</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] implies <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() ) &amp; ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] implies <font color="Maroon">F<sub>4</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() ) )
 
<b>by </b><i><a class="txt" href="yellow15.html#E1:1"><i><font color="Green">E1</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>1</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()<b> such that </b><br/><a NAME="E3:1_1"/><i><font color="Green">E3</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] implies <font color="Maroon">c<sub>1</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">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) ) &amp; ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] implies <font color="Maroon">c<sub>1</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">F<sub>4</sub></font>(<font color="Olive">b<sub>1</sub></font>) ) )
 <b>from </b><i><a class="ref" href="funct_2.html#S5">FUNCT_2:sch 5</a>(<a class="txt" href="yellow15.html#E1:1_1"><i><font color="Green">E2</font></i></a>);<br/></i>
<a NAME="E4:1_1"/><i><font color="Green">E4</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">F<sub>1</sub></font>()
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="finseq_1.html#NM1">FinSequence</a> <b>by </b><i><a class="ref" href="finseq_1.html#D2">FINSEQ_1:def 2</a></i>;<br/>
<a NAME="E6:1_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>()
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">F<sub>2</sub></font>() <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E8:1_1"/>
(  <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">F<sub>1</sub></font>() &amp; ( 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">F<sub>1</sub></font>() holds <br/>( ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] implies <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">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) ) &amp; ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] implies <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">F<sub>4</sub></font>(<font color="Olive">b<sub>1</sub></font>) ) ) ) )
 <b>by </b><i><a class="txt" href="yellow15.html#E3:1_1"><i><font color="Green">E3</font></i></a>, <a class="txt" href="yellow15.html#E4:1_1"><i><font color="Green">E4</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>


</div>
