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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM3">Subset-Family</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="rcomp_3.html#M1" target="_self">IntervalCover</a> of <font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="rcomp_3.html#M2" target="_self">IntervalCoverPts</a> of <font color="Maroon">c<sub>5</sub></font>;<br/>











<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:102"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="pre_topc.html#R1">is_a_cover_of</a>  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:102"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="tops_2.html#V1">open</a>
 <b>and </b><br/><a NAME="E3:102"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="rcomp_3.html#V1" target="_self">connected</a>
 <b>and </b><br/><a NAME="E4:102"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E5:102"/><i><font color="Green">E76</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E6:102"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E7:102"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E6:102"><i><font color="Green">E77</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E8:102"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is   <a href="nat_1.html#NM1">Nat</a>
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E9:102"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E5:102"><i><font color="Green">E76</font></i></a>, <a class="txt" href="rcomp_3.html#E6:102"><i><font color="Green">E77</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E10:102"/>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E11:102"/><b>then </b><i><font color="Green">E81</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E7:102"><i><font color="Green">E78</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E12:102"/><i><font color="Green">E82</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> <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>5</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="rcomp_3.html#D3" target="_self">Def3</a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a></i>;<br/>
<a NAME="E13:102"/><b>then </b><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E6:102"><i><font color="Green">E77</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E14:102"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E5:102"><i><font color="Green">E76</font></i></a>, <a class="txt" href="rcomp_3.html#E8:102"><i><font color="Green">E79</font></i></a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E15:102"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E5:102"><i><font color="Green">E76</font></i></a>, <a class="txt" href="rcomp_3.html#E13:102"><i><font color="Green">E83</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E16:102"/><b>then </b><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E17:102"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="rcomp_3.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E18:102"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E84</font></i></a>, <a class="txt" href="rcomp_3.html#E16:102"><i><font color="Green">E85</font></i></a></i>;<br/>
<a NAME="E19:102"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> is  <a href="connsp_1.html#V2">connected</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="ref" href="rcomp_3.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E20:102"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> is <a href="jct_misc.html#V1">connected</a>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T56" target="_self">Th56</a></i>;<br/>
<a NAME="E21:102"/><i><font color="Green">E87</font></i>: 
not <font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E5:102"><i><font color="Green">E76</font></i></a>, <a class="txt" href="rcomp_3.html#E13:102"><i><font color="Green">E83</font></i></a>, <a class="ref" href="rcomp_3.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E22:102"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:102_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>2</sub></font> )
 </span><b>by </b><i><a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1_1"><b>suppose </b></a><a NAME="E1:102_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:102_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="rcomp_1.html#K1">.]</a></span></span><a href="binarith.html#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="ref" href="rcomp_3.html#T64" target="_self">Th64</a></i>;<br/><a NAME="E3:102_1_1"/><b>then </b><i><font color="Green">E89</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/><a NAME="E4:102_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="rcomp_3.html#T75" target="_self">Th75</a></i>;<br/><a NAME="E5:102_1_1"/><b>then </b><i><font color="Green">E90</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/><a NAME="E6:102_1_1"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="rcomp_3.html#E3:102_1_1"><i><font color="Green">E89</font></i></a>, <a class="txt" href="rcomp_3.html#E13:102"><i><font color="Green">E83</font></i></a>, <a class="txt" href="rcomp_3.html#E5:102"><i><font color="Green">E76</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:102_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K1">.]</a></span></span><a href="binarith.html#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102_1_1"><i><font color="Green">E89</font></i></a>, <a class="ref" href="rcomp_3.html#T66" target="_self">Th66</a></i>;<br/><b>hence </b><a NAME="E8:102_1_1"/>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E6:102_1_1"><i><font color="Green">E91</font></i></a>, <a class="txt" href="rcomp_3.html#E5:102_1_1"><i><font color="Green">E90</font></i></a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1_2"><b>suppose </b></a><a NAME="E1:102_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:102_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> is <a href="seqm_3.html#V1">increasing</a>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="ref" href="rcomp_3.html#T79" target="_self">Th79</a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E3:102_1_2"/><b>then </b><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E22:102"><i><font color="Green">E88</font></i></a>, <a class="txt" href="rcomp_3.html#E9:102"><i><font color="Green">E80</font></i></a>, <a class="txt" href="rcomp_3.html#E11:102"><i><font color="Green">E81</font></i></a>, <a class="ref" href="seqm_3.html#D1">SEQM_3:def 1</a></i>;<br/><a NAME="E4:102_1_2"/><i><font color="Green">E90</font></i>: 
2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="rcomp_3.html#T74" target="_self">Th74</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:102_1_2_1"/>
( ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 2 ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; 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>6</sub></font> ) or ( 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1 ) or ( 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="rcomp_3.html#E5:102"><i><font color="Green">E76</font></i></a>, <a class="txt" href="rcomp_3.html#E7:102"><i><font color="Green">E78</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1_2_1_1"><b>suppose </b></a><b>that </b><a NAME="E1:102_1_2_1_1"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E2:102_1_2_1_1"/><i><font color="Green">E92</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><a NAME="E3:102_1_2_1_1"/><i><font color="Green">E93</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 2 <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="rcomp_3.html#E12:102"><i><font color="Green">E82</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102_1_2_1_1"><i><font color="Green">E92</font></i></a></i>;<br/><a NAME="E4:102_1_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="rcomp_3.html#T75" target="_self">Th75</a></i>;<br/><a NAME="E5:102_1_2_1_1"/><b>then </b><i><font color="Green">E94</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/><a NAME="E6:102_1_2_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="rcomp_1.html#K1">.]</a></span></span><a href="binarith.html#K13">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102_1_2_1_1"><i><font color="Green">E93</font></i></a>, <a class="ref" href="rcomp_3.html#T66" target="_self">Th66</a></i>;<br/><b>hence </b><a NAME="E7:102_1_2_1_1"/>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102_1_2_1_1"><i><font color="Green">E91</font></i></a>, <a class="txt" href="rcomp_3.html#E5:102_1_2_1_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1_2_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:102_1_2_1_2"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E2:102_1_2_1_2"/><i><font color="Green">E92</font></i>: 
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>6</sub></font>
 ;<br/><div class="add"><a NAME="E3:102_1_2_1_2"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K3">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p4">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K2">sup</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="rcomp_3.html#D3" target="_self">Def3</a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102_1_2_1_2"><i><font color="Green">E92</font></i></a></i>;<br/><a NAME="E4:102_1_2_1_2"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="rcomp_3.html#D3" target="_self">Def3</a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E5:102_1_2_1_2"/><i><font color="Green">E95</font></i>: 
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>5</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E2:102_1_2_1_2"><i><font color="Green">E92</font></i></a>, <a class="txt" href="rcomp_3.html#E12:102"><i><font color="Green">E82</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E6:102_1_2_1_2"/><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> 1
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="ref" href="rcomp_3.html#T71" target="_self">Th71</a></i>;<br/><a NAME="E7:102_1_2_1_2"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102_1_2_1_2"><i><font color="Green">E92</font></i></a>, <a class="txt" href="rcomp_3.html#E1:102_1_2_1_2"><i><font color="Green">E91</font></i></a>, <a class="ref" href="rcomp_3.html#T76" target="_self">Th76</a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E8:102_1_2_1_2"/><i><font color="Green">E98</font></i>: 
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E5:102_1_2_1_2"><i><font color="Green">E95</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="ref" href="rcomp_3.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E9:102_1_2_1_2"/>
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> 2
 <b>by </b><i><a class="txt" href="rcomp_3.html#E3:102_1_2_1_2"><i><font color="Green">E93</font></i></a>, <a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/><a NAME="E10:102_1_2_1_2"/><b>then </b>
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102_1_2_1_2"><i><font color="Green">E91</font></i></a>, <a class="txt" href="rcomp_3.html#E8:102_1_2_1_2"><i><font color="Green">E98</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E11:102_1_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E7:102_1_2_1_2"><i><font color="Green">E97</font></i></a>, <a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E84</font></i></a>, <a class="txt" href="rcomp_3.html#E21:102"><i><font color="Green">E87</font></i></a>, <a class="txt" href="rcomp_3.html#E20:102"><i><font color="Green">E86</font></i></a>, <a class="ref" href="rcomp_3.html#T42" target="_self">Th42</a></i>;<br/><b>hence </b><a NAME="E12:102_1_2_1_2"/>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102_1_2_1_2"><i><font color="Green">E91</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102_1_2_1_2"><i><font color="Green">E94</font></i></a>, <a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E84</font></i></a>, <a class="txt" href="rcomp_3.html#E6:102_1_2_1_2"><i><font color="Green">E96</font></i></a>, <a class="txt" href="rcomp_3.html#E20:102"><i><font color="Green">E86</font></i></a>, <a class="ref" href="jct_misc.html#D1">JCT_MISC:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1_2_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:102_1_2_1_3"/><i><font color="Green">E91</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:102_1_2_1_3"/><i><font color="Green">E92</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1
 ;<br/><div class="add"><a NAME="E3:102_1_2_1_3"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="ref" href="rcomp_3.html#D3" target="_self">Def3</a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E4:102_1_2_1_3"/><i><font color="Green">E94</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E12:102"><i><font color="Green">E82</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102_1_2_1_3"><i><font color="Green">E92</font></i></a></i>;<br/><a NAME="E5:102_1_2_1_3"/><b>then </b><i><font color="Green">E95</font></i>: 
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E1:102_1_2_1_3"><i><font color="Green">E91</font></i></a>, <a class="ref" href="rcomp_3.html#T77" target="_self">Th77</a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E6:102_1_2_1_3"/><i><font color="Green">E96</font></i>: 
1 <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102_1_2_1_3"><i><font color="Green">E91</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E7:102_1_2_1_3"/><b>then </b><i><font color="Green">E97</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="int_1.html#T20">INT_1:20</a></i>;<br/><a NAME="E8:102_1_2_1_3"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> 1 is   <a href="nat_1.html#NM1">Nat</a>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E6:102_1_2_1_3"><i><font color="Green">E96</font></i></a>, <a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E9:102_1_2_1_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K3">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pscomp_1.html#K2">sup</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E7:102_1_2_1_3"><i><font color="Green">E97</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102_1_2_1_3"><i><font color="Green">E92</font></i></a>, <a class="txt" href="rcomp_3.html#E22:102"><i><font color="Green">E88</font></i></a>, <a class="ref" href="rcomp_3.html#D3" target="_self">Def3</a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E10:102_1_2_1_3"/><b>then </b><i><font color="Green">E99</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/><a NAME="E11:102_1_2_1_3"/>
 <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102_1_2_1_3"><i><font color="Green">E94</font></i></a>, <a class="txt" href="rcomp_3.html#E8:102_1_2_1_3"><i><font color="Green">E98</font></i></a>, <a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E7:102_1_2_1_3"><i><font color="Green">E97</font></i></a>, <a class="ref" href="rcomp_3.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E12:102_1_2_1_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E10:102_1_2_1_3"><i><font color="Green">E99</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E13:102_1_2_1_3"/><b>then </b><i><font color="Green">E100</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E5:102_1_2_1_3"><i><font color="Green">E95</font></i></a>, <a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E84</font></i></a>, <a class="txt" href="rcomp_3.html#E21:102"><i><font color="Green">E87</font></i></a>, <a class="txt" href="rcomp_3.html#E20:102"><i><font color="Green">E86</font></i></a>, <a class="ref" href="rcomp_3.html#T42" target="_self">Th42</a></i>;<br/><a NAME="E14:102_1_2_1_3"/>
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E12:102"><i><font color="Green">E82</font></i></a>, <a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E84</font></i></a>, <a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102_1_2_1_3"><i><font color="Green">E93</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102_1_2_1_3"><i><font color="Green">E94</font></i></a>, <a class="ref" href="rcomp_3.html#T73" target="_self">Th73</a></i>;<br/><b>hence </b><a NAME="E15:102_1_2_1_3"/>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E13:102_1_2_1_3"><i><font color="Green">E100</font></i></a>, <a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E84</font></i></a>, <a class="txt" href="rcomp_3.html#E20:102"><i><font color="Green">E86</font></i></a>, <a class="ref" href="jct_misc.html#D1">JCT_MISC:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1_2_1_4"><b>suppose </b></a><b>that </b><a NAME="E1:102_1_2_1_4"/><i><font color="Green">E91</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:102_1_2_1_4"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><a NAME="E3:102_1_2_1_4"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E6:102"><i><font color="Green">E77</font></i></a>, <a class="txt" href="rcomp_3.html#E12:102"><i><font color="Green">E82</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:102_1_2_1_4"/><b>then </b><i><font color="Green">E93</font></i>: 
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E1:102_1_2_1_4"><i><font color="Green">E91</font></i></a>, <a class="ref" href="rcomp_3.html#T77" target="_self">Th77</a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E5:102_1_2_1_4"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E1:102"><i><font color="Green">E72</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102"><i><font color="Green">E73</font></i></a>, <a class="txt" href="rcomp_3.html#E4:102"><i><font color="Green">E75</font></i></a>, <a class="txt" href="rcomp_3.html#E5:102"><i><font color="Green">E76</font></i></a>, <a class="txt" href="rcomp_3.html#E2:102_1_2_1_4"><i><font color="Green">E92</font></i></a>, <a class="ref" href="rcomp_3.html#T76" target="_self">Th76</a>, <a class="txt" href="rcomp_3.html#E3:102"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E6:102_1_2_1_4"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K2">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E3:102_1_2"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E7:102_1_2_1_4"/><b>then </b><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E4:102_1_2_1_4"><i><font color="Green">E93</font></i></a>, <a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E84</font></i></a>, <a class="txt" href="rcomp_3.html#E21:102"><i><font color="Green">E87</font></i></a>, <a class="txt" href="rcomp_3.html#E20:102"><i><font color="Green">E86</font></i></a>, <a class="ref" href="rcomp_3.html#T42" target="_self">Th42</a></i>;<br/><a NAME="E8:102_1_2_1_4"/>
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E4:102_1_2_1_4"><i><font color="Green">E93</font></i></a>, <a class="txt" href="rcomp_3.html#E3:102_1_2"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E9:102_1_2_1_4"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E5:102_1_2_1_4"><i><font color="Green">E94</font></i></a>, <a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E84</font></i></a>, <a class="txt" href="rcomp_3.html#E21:102"><i><font color="Green">E87</font></i></a>, <a class="txt" href="rcomp_3.html#E20:102"><i><font color="Green">E86</font></i></a>, <a class="ref" href="rcomp_3.html#T42" target="_self">Th42</a></i>;<br/><b>hence </b><a NAME="E10:102_1_2_1_4"/>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span></span><a href="rcomp_1.html#K1">.]</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E84</font></i></a>, <a class="txt" href="rcomp_3.html#E7:102_1_2_1_4"><i><font color="Green">E95</font></i></a>, <a class="txt" href="rcomp_3.html#E20:102"><i><font color="Green">E86</font></i></a>, <a class="ref" href="jct_misc.html#D1">JCT_MISC:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

</div>
