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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="struct_0.html#NM8">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="jordan3.html#K2">Index</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>
<b>assume </b><a NAME="E1:30"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K5">L~</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:30"/><b>then </b><i><font color="Green">E18</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="jordan3.html#K2">Index</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp;  <a href="jordan3.html#K2">Index</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</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="jordan3.html#T41">JORDAN3:41</a></i>;<br/>
<a NAME="E3:30"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/>
<a NAME="E4:30"/><b>then </b><i><font color="Green">E19</font></i>: 
1 <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_5.html#T6">FINSEQ_5:6</a></i>;<br/>
<a NAME="E5:30"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 1 or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 1 )
 
;<br/>
<a NAME="E6:30"/><b>then </b>
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K4">R_Cut</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="jordan3.html#K2">Index</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> or  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K4">R_Cut</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan3.html#K2">Index</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="txt" href="sprect_3.html#E1:30"><i><font color="Green">E17</font></i></a>, <a class="ref" href="jordan3.html#T60">JORDAN3:60</a></i>;<br/>
<a NAME="E7:30"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K4">R_Cut</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="sprect_3.html#E1:30"><i><font color="Green">E17</font></i></a>, <a class="ref" href="jordan3.html#T41">JORDAN3:41</a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="jordan3.html#K4">R_Cut</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 = 
<span class="p1">(<span class="default"><a href="jordan3.html#K4">R_Cut</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="sprect_3.html#E1:30"><i><font color="Green">E17</font></i></a>, <a class="txt" href="sprect_3.html#E2:30"><i><font color="Green">E18</font></i></a>, <a class="ref" href="jordan3.html#T59">JORDAN3:59</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K4">/.</a> 1
<b>by </b><i><a class="txt" href="sprect_3.html#E4:30"><i><font color="Green">E19</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><br/>


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