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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<div><i><font color="Green">E13</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:24_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_8.html#R1" target="_self">separates_uniquely</a> 
 ;<br/><b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><a NAME="E2:24_1"/><i><font color="Green">E15</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#T52">BINARITH:52</a></i>;<br/><a NAME="E3:24_1"/><i><font color="Green">E16</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="finseq_8.html#T16" target="_self">Th16</a></i>;<br/><i><font color="Green">E17</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfinseq.html#T21">RFINSEQ:21</a></i>
;<br/><i><font color="Green">E18</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_8.html#T11" target="_self">Th11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T45">FINSEQ_1:45</a></i>
;<br/><i><font color="Green">E19</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E2:24_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="finseq_1.html#T80">FINSEQ_1:80</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E3:24_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfinseq.html#T21">RFINSEQ:21</a></i>
;<br/><a NAME="E7:24_1"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="finseq_8.html#T16" target="_self">Th16</a></i>;<br/><a NAME="E8:24_1"/><b>then </b><i><font color="Green">E20</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E9:24_1"/><i><font color="Green">E21</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>;<br/><a NAME="E10:24_1"/><i><font color="Green">E22</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="finseq_8.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E11:24_1"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <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>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><i><font color="Green">E24</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_8.html#T15" target="_self">Th15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T35">FINSEQ_1:35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rfinseq.html#T21">RFINSEQ:21</a></i>
;<br/><b>set </b><font color="Maroon">c<sub>5</sub></font> = 1;<br/><b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>;<br/><a NAME="E13:24_1"/><i><font color="Green">E25</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <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>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E14:24_1"/><i><font color="Green">E26</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="finseq_8.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E15:24_1"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <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>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="finseq_8.html#E13:24_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>then </b><i><font color="Green">E28</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E14:24_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/><a NAME="E17:24_1"/><b>then </b><i><font color="Green">E29</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><i><font color="Green">E30</font></i>:  <a href="finseq_8.html#K2" target="_self">smid</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> = 
 <a href="finseq_8.html#K2" target="_self">smid</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,1,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> 0</span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E9:24_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#T31">FINSEQ_5:31</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="finseq_8.html#E4:24_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="finseq_5.html#T26">FINSEQ_5:26</a></i>
;<br/><a NAME="E19:24_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E17:24_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><b>then </b><i><font color="Green">E31</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K3">+</a> 1
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>

;<br/><a NAME="E21:24_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><b>then </b><i><font color="Green">E32</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p0">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E20:24_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>

;<br/><a NAME="E23:24_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E24:24_1"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E10:24_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E25:24_1"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E26:24_1"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E11:24_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E27:24_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E11:24_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E14:24_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/><b>then </b><i><font color="Green">E33</font></i>:  <a href="finseq_8.html#K2" target="_self">smid</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E22:24_1"><i><font color="Green">E32</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E5:24_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="finseq_8.html#E6:24_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="finseq_8.html#E8:24_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="finseq_5.html#T40">FINSEQ_5:40</a></i>
<br/>.= 
 <a href="finseq_8.html#K2" target="_self">smid</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="finseq_1.html#K17">|</a> 1</span>)</span> <a href="finseq_8.html#K1" target="_self">^</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K4" target="_self">ovlcon</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E18:24_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_1.html#T79">FINSEQ_1:79</a></i>
;<br/><a NAME="E30:24_1"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="finseq_8.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E31:24_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <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>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="ref" href="jordan3.html#T19">JORDAN3:19</a></i>;<br/><a NAME="E32:24_1"/><b>then </b><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_11"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_11_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_1_11_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_11_1_1"><b>case </b></a><a NAME="E1:24_1_11_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 ;<br/><div class="add"><b>then </b><span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> = 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
1 <a href="nat_1.html#K1">+</a> 1

;<br/><a NAME="E3:24_1_11_1_1"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E32:24_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E4:24_1_11_1_1"/><b>then </b><i><font color="Green">E35</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E15:24_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E5:24_1_11_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1 <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>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>;<br/><a NAME="E6:24_1_11_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <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>2</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E14:24_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E7:24_1_11_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="finseq_8.html#E12:24_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="finseq_8.html#E16:24_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="finseq_8.html#E18:24_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="finseq_8.html#E29:24_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="finseq_8.html#E4:24_1_11_1_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="finseq_8.html#D6" target="_self">Def6</a></i>;<br/><i><font color="Green">E37</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 = 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E16:24_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="finseq_8.html#E17:24_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>

;<br/><a NAME="E9:24_1_11_1_1"/><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="binarith.html#T52">BINARITH:52</a></i>;<br/><a NAME="E10:24_1_11_1_1"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E14:24_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E11:24_1_11_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E7:24_1_11_1_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="finseq_8.html#E8:24_1_11_1_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="finseq_8.html#E9:24_1_11_1_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><b>hence </b><a NAME="E12:24_1_11_1_1"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_11_1_2"><b>case </b></a><a NAME="E1:24_1_11_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1
 ;<br/><div class="add"><a NAME="E2:24_1_11_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 0 <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E3:24_1_11_1_2"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:24_1_11_1_2"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="finseq_8.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E5:24_1_11_1_2"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="finseq_8.html#E3:24_1_11_1_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E34:24_1"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:24_2"/><i><font color="Green">E14</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:24_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="finseq_8.html#K2" target="_self">smid</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_8.html#K2" target="_self">smid</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> &amp;  <a href="finseq_8.html#K2" target="_self">smid</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="binarith.html#K5">-'</a> <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:24_2_1"/><i><font color="Green">E15</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="finseq_8.html#K2" target="_self">smid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_8.html#K2" target="_self">smid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> &amp;  <a href="finseq_8.html#K2" target="_self">smid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:24_2_1"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/>
<a NAME="E3:24_2_1"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<i><font color="Green">E18</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="finseq_8.html#E2:24_2_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font>

;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_2_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_2_1_2_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 or  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_2_1_2_1_1"><b>case </b></a><a NAME="E1:24_2_1_2_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:24_2_1_2_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_2_1_2_1_2"><b>case </b></a><a NAME="E1:24_2_1_2_1_2"/><i><font color="Green">E19</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E20</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E3:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E21</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E4:24_2_1_2_1_2"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E2:24_2_1_2_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E5:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E6:24_2_1_2_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E7:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E24</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="finseq_8.html#E3:24_2_1_2_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="finseq_8.html#E5:24_2_1_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font>;<br/><a NAME="E8:24_2_1_2_1_2"/><i><font color="Green">E25</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E2:24_2_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="finseq_8.html#E3:24_2_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E9:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E26</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><i><font color="Green">E27</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E8:24_2_1_2_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E2:24_2_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> 1

;<br/><a NAME="E11:24_2_1_2_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E12:24_2_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E13:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a></i>;<br/><a NAME="E14:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E15:24_2_1_2_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/><a NAME="E16:24_2_1_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E17:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E18:24_2_1_2_1_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E19:24_2_1_2_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E20:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E21:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E33</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E13:24_2_1_2_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E21:24_2_1_2_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/><a NAME="E23:24_2_1_2_1_2"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="finseq_8.html#E10:24_2_1_2_1_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="finseq_8.html#E14:24_2_1_2_1_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="finseq_8.html#E18:24_2_1_2_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2_1_2_1_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:24_2_1_2_1_2_3"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:24_2_1_2_1_2_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1 <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>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E3:24_2_1_2_1_2_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1 <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>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="finseq_8.html#E17:24_2_1_2_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E4:24_2_1_2_1_2_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1 <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>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="finseq_8.html#E2:24_2_1_2_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E5:24_2_1_2_1_2_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <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>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E6:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font> <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>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="finseq_8.html#E9:24_2_1_2_1_2"><i><font color="Green">E26</font></i></a></i>;<br/><a NAME="E7:24_2_1_2_1_2_3"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <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>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1_2_1_2_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E8:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E38</font></i>: 
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>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><a NAME="E9:24_2_1_2_1_2_3"/>
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>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E7:24_2_1_2_1_2_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E10:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E39</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <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>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E11:24_2_1_2_1_2_3"/><i><font color="Green">E40</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E7:24_2_1_2_1_2_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E12:24_2_1_2_1_2_3"/><i><font color="Green">E41</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E8:24_2_1_2_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="finseq_8.html#E1:24_2_1_2_1_2_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E13:24_2_1_2_1_2_3"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E14:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1 <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>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E15:24_2_1_2_1_2_3"/><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="finseq_8.html#E12:24_2_1_2_1_2_3"><i><font color="Green">E41</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E16:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <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>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="finseq_8.html#E8:24_2_1_2_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="finseq_8.html#E11:24_2_1_2_1_2_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="real_2.html#T106">REAL_2:106</a></i>;<br/><a NAME="E17:24_2_1_2_1_2_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E18:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E23:24_2_1_2_1_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E19:24_2_1_2_1_2_3"/>
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="finseq_8.html#E20:24_2_1_2_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span>

<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E2:24_2_1_2_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/><a NAME="E21:24_2_1_2_1_2_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E22:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E23:24_2_1_2_1_2_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E24:24_2_1_2_1_2_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E25:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E26:24_2_1_2_1_2_3"/><i><font color="Green">E48</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E27:24_2_1_2_1_2_3"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1_2_1_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="xreal_1.html#T31">XREAL_1:31</a></i>;<br/><a NAME="E28:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E50</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E26:24_2_1_2_1_2_3"><i><font color="Green">E48</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E29:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/><a NAME="E30:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="finseq_8.html#E25:24_2_1_2_1_2_3"><i><font color="Green">E47</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E31:24_2_1_2_1_2_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E32:24_2_1_2_1_2_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E5:24_2_1_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><a NAME="E33:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E30:24_2_1_2_1_2_3"><i><font color="Green">E52</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E34:24_2_1_2_1_2_3"/>
0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="finseq_8.html#E28:24_2_1_2_1_2_3"><i><font color="Green">E50</font></i></a>, <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/><a NAME="E35:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E54</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="txt" href="finseq_8.html#E29:24_2_1_2_1_2_3"><i><font color="Green">E51</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E36:24_2_1_2_1_2_3"/>
<font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E27:24_2_1_2_1_2_3"><i><font color="Green">E49</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E37:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E38:24_2_1_2_1_2_3"/><i><font color="Green">E56</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font> <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>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/><a NAME="E39:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E57</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><a NAME="E40:24_2_1_2_1_2_3"/><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="finseq_8.html#E11:24_2_1_2_1_2_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="finseq_8.html#E38:24_2_1_2_1_2_3"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><a NAME="E41:24_2_1_2_1_2_3"/><i><font color="Green">E59</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K2" target="_self">smid</a> <font color="Maroon">c<sub>2</sub></font>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>2</sub></font>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E10:24_2_1_2_1_2_3"><i><font color="Green">E39</font></i></a>, <a class="ref" href="finseq_8.html#T4" target="_self">Th4</a></i>;<br/><i><font color="Green">E60</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>2</sub></font>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E2:24_2_1_2_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="finseq_8.html#E10:24_2_1_2_1_2_3"><i><font color="Green">E39</font></i></a>, <a class="txt" href="finseq_8.html#E11:24_2_1_2_1_2_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="finseq_8.html#E39:24_2_1_2_1_2_3"><i><font color="Green">E57</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K3">+</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E10:24_2_1_2_1_2_3"><i><font color="Green">E39</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>

;<br/><i><font color="Green">E61</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="jordan3.html#T19">JORDAN3:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E16:24_2_1_2_1_2_3"><i><font color="Green">E44</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E11:24_2_1_2_1_2_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="finseq_8.html#E12:24_2_1_2_1_2_3"><i><font color="Green">E41</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font>

;<br/><a NAME="E44:24_2_1_2_1_2_3"/><i><font color="Green">E62</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1
 <b>by </b><i><a class="ref" href="jordan3.html#T19">JORDAN3:19</a></i>;<br/><a NAME="E45:24_2_1_2_1_2_3"/><b>then </b><i><font color="Green">E63</font></i>: 
 <a href="finseq_8.html#K2" target="_self">smid</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="jordan3.html#K1">mid</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E6:24_2_1_2_1_2_3"><i><font color="Green">E36</font></i></a>, <a class="txt" href="finseq_8.html#E43:24_2_1_2_1_2_3"><i><font color="Green">E61</font></i></a>, <a class="ref" href="finseq_8.html#T4" target="_self">Th4</a></i>;<br/><i><font color="Green">E64</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E8:24_2_1_2_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="finseq_8.html#E6:24_2_1_2_1_2_3"><i><font color="Green">E36</font></i></a>, <a class="txt" href="finseq_8.html#E14:24_2_1_2_1_2_3"><i><font color="Green">E42</font></i></a>, <a class="txt" href="finseq_8.html#E15:24_2_1_2_1_2_3"><i><font color="Green">E43</font></i></a>, <a class="txt" href="finseq_8.html#E44:24_2_1_2_1_2_3"><i><font color="Green">E62</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E6:24_2_1_2_1_2_3"><i><font color="Green">E36</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E12:24_2_1_2_1_2_3"><i><font color="Green">E41</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E7:24_2_1_2_1_2_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/><a NAME="E47:24_2_1_2_1_2_3"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <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>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="finseq_8.html#K2" target="_self">smid</a> <font color="Maroon">c<sub>2</sub></font>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K2" target="_self">smid</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2_1_2_1_2_3_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:24_2_1_2_1_2_3_5"/><i><font color="Green">E65</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <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>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> )
 ;<br/>

<a NAME="E2:24_2_1_2_1_2_3_5"/><b>then </b><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E3:24_2_1_2_1_2_3_5"/><b>then </b><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <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>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1
 
<b>by </b><i><a class="txt" href="finseq_8.html#E11:24_2_1_2_1_2_3"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<i><font color="Green">E68</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="finseq_8.html#E3:24_2_1_2_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="finseq_8.html#E5:24_2_1_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="finseq_8.html#E6:24_2_1_2_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="finseq_8.html#E7:24_2_1_2_1_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="finseq_8.html#E18:24_2_1_2_1_2_3"><i><font color="Green">E45</font></i></a>, <a class="txt" href="finseq_8.html#E33:24_2_1_2_1_2_3"><i><font color="Green">E53</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K3">+</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E3:24_2_1_2_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="finseq_8.html#E5:24_2_1_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="finseq_8.html#E6:24_2_1_2_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>

;<br/>
<a NAME="E5:24_2_1_2_1_2_3_5"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="binarith.html#T52">BINARITH:52</a></i>;<br/>
<a NAME="E6:24_2_1_2_1_2_3_5"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1_2_1_2_3_5"><i><font color="Green">E65</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E7:24_2_1_2_1_2_3_5"/><i><font color="Green">E70</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1_2_1_2_3_5"><i><font color="Green">E65</font></i></a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<a NAME="E8:24_2_1_2_1_2_3_5"/><i><font color="Green">E71</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1_2_1_2_3_5"><i><font color="Green">E65</font></i></a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<i><font color="Green">E72</font></i>: <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> = 
<font color="Maroon">c<sub>8</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E8:24_2_1_2_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1
<b>by </b><i><a class="txt" href="finseq_8.html#E7:24_2_1_2_1_2_3_5"><i><font color="Green">E70</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
;<br/>
<a NAME="E10:24_2_1_2_1_2_3_5"/><i><font color="Green">E73</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1_2_1_2_3_5"><i><font color="Green">E65</font></i></a>, <a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<a NAME="E11:24_2_1_2_1_2_3_5"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <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>2</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1
 
<b>by </b><i><a class="txt" href="finseq_8.html#E3:24_2_1_2_1_2_3_5"><i><font color="Green">E67</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E12:24_2_1_2_1_2_3_5"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <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>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1
 
<b>by </b><i><a class="txt" href="finseq_8.html#E2:24_2_1_2_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E13:24_2_1_2_1_2_3_5"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_8.html#E44:24_2_1_2_1_2_3"><i><font color="Green">E62</font></i></a>, <a class="txt" href="finseq_8.html#E8:24_2_1_2_1_2_3_5"><i><font color="Green">E71</font></i></a>, <a class="txt" href="finseq_8.html#E9:24_2_1_2_1_2_3_5"><i><font color="Green">E72</font></i></a></i>;<br/>
<a NAME="E14:24_2_1_2_1_2_3_5"/><b>then </b><i><font color="Green">E74</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E15:24_2_1_2_1_2_3_5"/><i><font color="Green">E75</font></i>: 
 <a href="finseq_8.html#K2" target="_self">smid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="finseq_8.html#E29:24_2_1_2_1_2_3"><i><font color="Green">E51</font></i></a>, <a class="txt" href="finseq_8.html#E37:24_2_1_2_1_2_3"><i><font color="Green">E55</font></i></a>, <a class="ref" href="finseq_8.html#T4" target="_self">Th4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="finseq_8.html#K2" target="_self">smid</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E8:24_2_1_2_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="finseq_8.html#E6:24_2_1_2_1_2_3"><i><font color="Green">E36</font></i></a>, <a class="txt" href="finseq_8.html#E14:24_2_1_2_1_2_3"><i><font color="Green">E42</font></i></a>, <a class="txt" href="finseq_8.html#E15:24_2_1_2_1_2_3"><i><font color="Green">E43</font></i></a>, <a class="txt" href="finseq_8.html#E44:24_2_1_2_1_2_3"><i><font color="Green">E62</font></i></a>, <a class="txt" href="finseq_8.html#E45:24_2_1_2_1_2_3"><i><font color="Green">E63</font></i></a>, <a class="txt" href="finseq_8.html#E46:24_2_1_2_1_2_3"><i><font color="Green">E64</font></i></a>, <a class="txt" href="finseq_8.html#E1:24_2_1_2_1_2_3_5"><i><font color="Green">E65</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_8.html#K2" target="_self">smid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="finseq_8.html#E2:24_2_1_2_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="finseq_8.html#E14:24_2_1_2_1_2_3_5"><i><font color="Green">E74</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E3:24_2_1_2_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="finseq_8.html#E5:24_2_1_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="finseq_8.html#E6:24_2_1_2_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="finseq_8.html#T4" target="_self">Th4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K3">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E10:24_2_1_2_1_2_3_5"><i><font color="Green">E73</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="finseq_8.html#E3:24_2_1_2_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="finseq_8.html#E5:24_2_1_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="finseq_8.html#E6:24_2_1_2_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="finseq_8.html#E7:24_2_1_2_1_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="finseq_8.html#E11:24_2_1_2_1_2_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="finseq_8.html#E18:24_2_1_2_1_2_3"><i><font color="Green">E45</font></i></a>, <a class="txt" href="finseq_8.html#E33:24_2_1_2_1_2_3"><i><font color="Green">E53</font></i></a>, <a class="txt" href="finseq_8.html#E2:24_2_1_2_1_2_3_5"><i><font color="Green">E66</font></i></a>, <a class="txt" href="finseq_8.html#E4:24_2_1_2_1_2_3_5"><i><font color="Green">E68</font></i></a>, <a class="txt" href="finseq_8.html#E10:24_2_1_2_1_2_3_5"><i><font color="Green">E73</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>

<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="finseq_8.html#E4:24_2_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="finseq_8.html#E22:24_2_1_2_1_2_3"><i><font color="Green">E46</font></i></a>, <a class="txt" href="finseq_8.html#E26:24_2_1_2_1_2_3"><i><font color="Green">E48</font></i></a>, <a class="txt" href="finseq_8.html#E29:24_2_1_2_1_2_3"><i><font color="Green">E51</font></i></a>, <a class="txt" href="finseq_8.html#E35:24_2_1_2_1_2_3"><i><font color="Green">E54</font></i></a>, <a class="txt" href="finseq_8.html#E37:24_2_1_2_1_2_3"><i><font color="Green">E55</font></i></a>, <a class="txt" href="finseq_8.html#E1:24_2_1_2_1_2_3_5"><i><font color="Green">E65</font></i></a>, <a class="txt" href="finseq_8.html#E6:24_2_1_2_1_2_3_5"><i><font color="Green">E69</font></i></a>, <a class="txt" href="finseq_8.html#E15:24_2_1_2_1_2_3_5"><i><font color="Green">E75</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="jordan3.html#K1">mid</a> <font color="Maroon">c<sub>2</sub></font>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="finseq_8.html#E2:24_2_1_2_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="finseq_8.html#E10:24_2_1_2_1_2_3"><i><font color="Green">E39</font></i></a>, <a class="txt" href="finseq_8.html#E11:24_2_1_2_1_2_3"><i><font color="Green">E40</font></i></a>, <a class="txt" href="finseq_8.html#E39:24_2_1_2_1_2_3"><i><font color="Green">E57</font></i></a>, <a class="txt" href="finseq_8.html#E42:24_2_1_2_1_2_3"><i><font color="Green">E60</font></i></a>, <a class="txt" href="finseq_8.html#E1:24_2_1_2_1_2_3_5"><i><font color="Green">E65</font></i></a>, <a class="ref" href="jordan3.html#T27">JORDAN3:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_8.html#K2" target="_self">smid</a> <font color="Maroon">c<sub>2</sub></font>,1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="finseq_8.html#E10:24_2_1_2_1_2_3"><i><font color="Green">E39</font></i></a>, <a class="ref" href="finseq_8.html#T4" target="_self">Th4</a></i>
;<br/>


</div><b>end;</b></div><a NAME="E48:24_2_1_2_1_2_3"/><b>then </b>
 <a href="finseq_8.html#K2" target="_self">smid</a> <font color="Maroon">c<sub>2</sub></font>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_8.html#K2" target="_self">smid</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E41:24_2_1_2_1_2_3"><i><font color="Green">E59</font></i></a>, <a class="txt" href="finseq_8.html#E42:24_2_1_2_1_2_3"><i><font color="Green">E60</font></i></a>, <a class="txt" href="finseq_8.html#E45:24_2_1_2_1_2_3"><i><font color="Green">E63</font></i></a>, <a class="txt" href="finseq_8.html#E46:24_2_1_2_1_2_3"><i><font color="Green">E64</font></i></a>, <a class="ref" href="finseq_1.html#T18">FINSEQ_1:18</a></i>;<br/><a NAME="E49:24_2_1_2_1_2_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="finseq_8.html#E40:24_2_1_2_1_2_3"><i><font color="Green">E58</font></i></a>, <a class="ref" href="finseq_8.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E50:24_2_1_2_1_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="finseq_8.html#E8:24_2_1_2_1_2_3"><i><font color="Green">E38</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E25:24_2_1_2_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:24_2_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="binarith.html#K5">-'</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:24_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="finseq_8.html#R1" target="_self">separates_uniquely</a> 
 <b>by </b><i><a class="ref" href="finseq_8.html#D6" target="_self">Def6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:24"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="finseq_8.html#R1" target="_self">separates_uniquely</a>  iff  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_8.html#K3" target="_self">ovlpart</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rfinseq.html#K1">/^</a> 1</span>)</span>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="txt" href="finseq_8.html#E1:24"><i><font color="Green">E13</font></i></a></i>;<br/>


</div>
