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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">f1</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>;<br/><b>let </b><font color="Maroon" title="c3">k1</font>, <font color="Maroon" title="c4">k2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:18_1_1"/>
( <font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">k2</font> or <font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">k2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1"><b>case </b></a><a NAME="E1:18_1_1_1"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">k2</font>
 ;<br/><div class="add"><a NAME="E2:18_1_1_1"/><b>then </b><i><font color="Green" title="E22">A2</font></i>: 
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfinseq.html#K1" title="RFINSEQ:func.1">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">k1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="jordan3.html#D1" title="JORDAN3:def.1">JORDAN3:def 1</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:18_1_1_1_1_1"/>
( <font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">k2</font> or <font color="Maroon" title="c3">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k2</font> )
 </span><b>by </b><i><a class="txt" href="jordan4.html#E1:18_1_1_1"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1_1_1"><b>case </b></a><a NAME="E1:18_1_1_1_1_1_1"/>
<font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">k2</font>
 ;<br/><div class="add"><a NAME="E2:18_1_1_1_1_1_1"/><b>then </b>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan4.html#E2:18_1_1_1"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="jordan3.html#D1" title="JORDAN3:def.1">JORDAN3:def 1</a></i>;<br/><b>hence </b><a NAME="E3:18_1_1_1_1_1_1"/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_6.html#T29" title="FINSEQ_6:th.29">FINSEQ_6:29</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1_1_2"><b>case </b></a><a NAME="E1:18_1_1_1_1_1_2"/><i><font color="Green" title="E23">A3</font></i>: 
<font color="Maroon" title="c3">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k2</font>
 ;<br/><div class="add"><a NAME="E2:18_1_1_1_1_1_2"/>
( <font color="Maroon" title="c3">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 )
 <b>by </b><i><a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></i>;<br/><a NAME="E3:18_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E24">A4</font></i>: 
( <font color="Maroon" title="c3">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or 0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k1</font> )
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:18_1_1_1_1_1_2_1_1"/>
( <font color="Maroon" title="c3">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k1</font> &amp; <font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f1</font> ) or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k1</font> )
 </span><b>by </b><i><a class="txt" href="jordan4.html#E3:18_1_1_1_1_1_2"><i><font color="Green" title="E24">A4</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:18_1_1_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c3">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:18_1_1_1_1_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E25">A5</font></i>: 
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> 1
 <b>by </b><i><a class="txt" href="jordan4.html#E1:18_1_1_1_1_1_2"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="jordan4.html#T28" target="_self" title="JORDAN4:th.28">Th28</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1_1_1_1_2_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1_1_2_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:18_1_1_1_1_1_2_1_1_1_1_1"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1_1_2_1_1_1_1_1_1"><b>case </b></a><a NAME="E1:18_1_1_1_1_1_2_1_1_1_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:18_1_1_1_1_1_2_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c1">D</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T32" title="FINSEQ_1:th.32">FINSEQ_1:32</a></i>;<br/><a NAME="E3:18_1_1_1_1_1_2_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">f1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c1">D</font>
 <b>by </b><i><a class="ref" href="finseq_5.html#T81" title="FINSEQ_5:th.81">FINSEQ_5:81</a></i>;<br/><b>hence </b><a NAME="E4:18_1_1_1_1_1_2_1_1_1_1_1_1"/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan4.html#E1:18_1_1_1_1_1_2"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="jordan4.html#E2:18_1_1_1_1_1_2_1_1_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="finseq_5.html#T82" title="FINSEQ_5:th.82">FINSEQ_5:82</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1_1_2_1_1_1_1_1_2"><b>case </b></a><a NAME="E1:18_1_1_1_1_1_2_1_1_1_1_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:18_1_1_1_1_1_2_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">f1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c1">D</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T32" title="FINSEQ_1:th.32">FINSEQ_1:32</a></i>;<br/><a NAME="E3:18_1_1_1_1_1_2_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">f1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> 1</span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_5.html#T23" title="FINSEQ_5:th.23">FINSEQ_5:23</a></i>;<br/><b>hence </b><a NAME="E4:18_1_1_1_1_1_2_1_1_1_1_1_2"/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan4.html#E1:18_1_1_1_1_1_2"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="jordan4.html#E2:18_1_1_1_1_1_2_1_1_1"><i><font color="Green" title="E25">A5</font></i></a>, <a class="ref" href="finseq_5.html#T63" title="FINSEQ_5:th.63">FINSEQ_5:63</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:18_1_1_1_1_1_2_1_1_1"/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:18_1_1_1_1_1_2_1_1_2"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k1</font> &amp; <font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f1</font> )
 ;<br/><div class="add"><a NAME="E2:18_1_1_1_1_1_2_1_1_2"/><b>then </b>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c3">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c3">k1</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="jordan4.html#T27" target="_self" title="JORDAN4:th.27">Th27</a></i>;<br/><b>hence </b><a NAME="E3:18_1_1_1_1_1_2_1_1_2"/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan4.html#E1:18_1_1_1_1_1_2"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="finseq_5.html#T63" title="FINSEQ_5:th.63">FINSEQ_5:63</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1_1_2_1_1_3"><b>case </b></a><a NAME="E1:18_1_1_1_1_1_2_1_1_3"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">k1</font>
 ;<br/><div class="add"><a NAME="E2:18_1_1_1_1_1_2_1_1_3"/><b>then </b>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c3">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <font color="Maroon" title="c1">D</font>
 <b>by </b><i><a class="ref" href="jordan4.html#T29" target="_self" title="JORDAN4:th.29">Th29</a></i>;<br/><b>hence </b><a NAME="E3:18_1_1_1_1_1_2_1_1_3"/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan4.html#E1:18_1_1_1_1_1_2"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="finseq_5.html#T82" title="FINSEQ_5:th.82">FINSEQ_5:82</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:18_1_1_1_1_1_2"/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:18_1_1_1"/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_2"><b>case </b></a><a NAME="E1:18_1_1_2"/><i><font color="Green" title="E21">A6</font></i>: 
<font color="Maroon" title="c3">k1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">k2</font>
 ;<br/><div class="add"><a NAME="E2:18_1_1_2"/><b>then </b>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f1</font> <a href="rfinseq.html#K1" title="RFINSEQ:func.1">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">k1</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">k2</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="jordan3.html#D1" title="JORDAN3:def.1">JORDAN3:def 1</a></i>;<br/><b>hence </b><a NAME="E3:18_1_1_2"/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan4.html#E1:18_1_1_2"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="jordan3.html#D1" title="JORDAN3:def.1">JORDAN3:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:18"/>
 <a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c3">k1</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">mid</a> <font color="Maroon" title="c2">f1</font>,<font color="Maroon" title="c4">k2</font>,<font color="Maroon" title="c3">k1</font></span>)</span>
 ;<br/>


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