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

<b>reconsider </b><font color="Maroon">c<sub>1</sub></font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default">2,<span class="p3">(<span class="default"><a href="fib_num2.html#K2" target="_self">FIB</a>  <a href="funct_2.html#K3">.</a> 2</span>)</span></span><a href="domain_1.html#K1">]</a></span></span><a href="tarski.html#K1">}</a></span> as   <a href="funct_1.html#NM1">Function</a> <b>by </b><i><a class="ref" href="grfunc_1.html#T15">GRFUNC_1:15</a></i>;<br/>
<a NAME="E2:71"/><i><font color="Green">E52</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default">2</span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T23">RELAT_1:23</a></i>;<br/>
<a NAME="E3:71"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K2">Seg</a> 2
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</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="E1:71_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:71_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="txt" href="fib_num2.html#E2:71"><i><font color="Green">E52</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:71_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 2
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>


</div><b>end;</b></div>
<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#NM4">FinSubsequence</a> <b>by </b><i><a class="ref" href="finseq_1.html#D12">FINSEQ_1:def 12</a></i>;<br/>
<a NAME="E5:71"/>
2 <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 
;<br/>
<a NAME="E6:71"/><b>then </b>
2 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="fib_num2.html#K2" target="_self">FIB</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b> <a href="finseq_1.html#K15">Seq</a> <span class="p1">(<span class="default"><a href="fib_num2.html#K2" target="_self">FIB</a>  <a href="relat_1.html#K7">|</a> <span class="p2"><a href="seq_4.html#K1">{</a><span class="default">2</span><a href="seq_4.html#K1">}</a></span></span>)</span> = 
 <a href="finseq_1.html#K15">Seq</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="grfunc_1.html#T89">GRFUNC_1:89</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="fib_num2.html#K2" target="_self">FIB</a>  <a href="funct_2.html#K3">.</a> 2</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span>
<b>by </b><i><a class="ref" href="pnproc_1.html#T3">PNPROC_1:3</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default">1</span><a href="binarith.html#K13">*&gt;</a></span>
<b>by </b><i><a class="ref" href="fib_num2.html#D2" target="_self">Def2</a>, <a class="ref" href="fib_num2.html#T23" target="_self">Th23</a></i>
;<br/>
<b>hence </b><a NAME="E8:71"/>
 <a href="finseq_1.html#K15">Seq</a> <span class="p1">(<span class="default"><a href="fib_num2.html#K2" target="_self">FIB</a>  <a href="relat_1.html#K7">|</a> <span class="p2"><a href="seq_4.html#K1">{</a><span class="default">2</span><a href="seq_4.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default">1</span><a href="binarith.html#K13">*&gt;</a></span>
 ;<br/>


</div>
