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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>thus </b><a NAME="E1:24"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font> implies ( <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 is   <a href="nat_1.html#NM1">Nat</a> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font> is   <a href="nat_1.html#NM1">Nat</a> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:24_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:24_1"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> &amp; 1 is   <a href="int_1.html#NM1">Integer</a> &amp; <font color="Maroon">c<sub>2</sub></font> is   <a href="int_1.html#NM1">Integer</a> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> is   <a href="int_1.html#NM1">Integer</a> )
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27" target="_self">Th27</a></i>;<br/>
<b>hence </b><a NAME="E3:24_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 is   <a href="nat_1.html#NM1">Nat</a> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font> is   <a href="nat_1.html#NM1">Nat</a> )
 <b>by </b><i><a class="ref" href="int_1.html#T18">INT_1:18</a></i>;<br/>


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

<b>assume </b><a NAME="E2:24"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 is   <a href="nat_1.html#NM1">Nat</a> &amp; <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font> is   <a href="nat_1.html#NM1">Nat</a> )
 ;<br/>

<a NAME="E3:24"/><b>then </b>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>2</sub></font> )
 
;<br/>
<a NAME="E4:24"/><b>then </b>
( 0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; 0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/>
<b>hence </b><a NAME="E5:24"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T27" target="_self">Th27</a></i>;<br/>


</div>
