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<div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c1">H</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default">2,<span class="p3">(<span class="default"><a href="fib_num2.html#K2" title="FIB_NUM2:func.2">FIB</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 2</span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/>
<a NAME="E2:69"/><span class="lab"><font color="Green" title="E49">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">2</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T23" title="RELAT_1:th.23">RELAT_1:23</a></span>;<br/>
<a NAME="E3:69"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">H</font> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2 )</span><br/>

<span class="kw">assume </span><a NAME="E1:69_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2</span><br/>

<a NAME="E2:69_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:69_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">H</font> = <font color="Maroon" title="c1">H</font> as   <a href="finseq_1.html#NM4" title="FINSEQ_1:NM.4">FinSubsequence</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D12" title="FINSEQ_1:def.12">FINSEQ_1:def 12</a></span>;<br/>
<a NAME="E5:69"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
;<br/>
<a NAME="E6:69"/><span class="kw">then </span>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="fib_num2.html#K2" title="FIB_NUM2:func.2">FIB</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">then </span> <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <span class="p1">(<span class="default"><a href="fib_num2.html#K2" title="FIB_NUM2:func.2">FIB</a>  <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">2</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> = 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <font color="Maroon" title="c2">H</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="grfunc_1.html#T89" title="GRFUNC_1:th.89">GRFUNC_1:89</a></span>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="fib_num2.html#K2" title="FIB_NUM2:func.2">FIB</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 2</span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pnproc_1.html#T3" title="PNPROC_1:th.3">PNPROC_1:3</a></span>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="fib_num2.html#D2" target="_self" title="FIB_NUM2:def.2">Def2</a>, <a class="ref" href="fib_num2.html#T23" target="_self" title="FIB_NUM2:th.23">Th23</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:69"/>
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <span class="p1">(<span class="default"><a href="fib_num2.html#K2" title="FIB_NUM2:func.2">FIB</a>  <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">2</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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