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

<b>let </b><font color="Maroon">r</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">s</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">n</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">F</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">r</font>,<font color="Maroon">s</font></span>)</span>;<br/><b>let </b><font color="Maroon">C</font> be    <a href="rcomp_3.html#M1" target="_self">IntervalCover</a> of <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">G</font> be    <a href="rcomp_3.html#M2" target="_self">IntervalCoverPts</a> of <font color="Maroon">C</font>;<br/>











<b>set </b><font color="Maroon">L</font> =  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">r</font>,<font color="Maroon">s</font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:102"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> <a href="pre_topc.html#R1">is_a_cover_of</a>  <a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">r</font>,<font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E2:102"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">F</font> is <a href="tops_2.html#V1">open</a>
 <b>and </b><br/><a NAME="E3:102"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">F</font> is <a href="rcomp_3.html#V1" target="_self">connected</a>
 <b>and </b><br/><a NAME="E4:102"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E5:102"/><i><font color="Green">E46</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E6:102"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font>
 ;<br/>

<a NAME="E7:102"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">n</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">G</font>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T31" target="_self">Th31</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E8:102"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">n</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">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">E50</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">G</font>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T30" target="_self">Th30</a>, <a class="ref" href="rcomp_3.html#T31" target="_self">Th31</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">n</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">E51</font></i>: 
<font color="Maroon">n</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">G</font>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T32" target="_self">Th32</a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E12:102"/><i><font color="Green">E52</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</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</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="txt" href="rcomp_3.html#E22"><i><font color="Green">Lemma65</font></i></a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E13:102"/><b>then </b><i><font color="Green">E53</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T31" target="_self">Th31</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">E91</font></i>: 
<font color="Maroon">C</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T30" target="_self">Th30</a>, <a class="ref" href="rcomp_3.html#T33" target="_self">Th33</a>, <a class="ref" href="finseq_4.html#T24">FINSEQ_4:24</a></i>;<br/>
<a NAME="E15:102"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T30" target="_self">Th30</a>, <a class="ref" href="rcomp_3.html#T37" target="_self">Th37</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">E95</font></i>: 
<font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">C</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</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="ref" href="rcomp_3.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E18:102"/><b>then </b>
<font color="Maroon">C</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T38" target="_self">Th38</a>, <a class="ref" href="rcomp_3.html#T39" target="_self">Th39</a></i>;<br/>
<a NAME="E19:102"/><b>then </b>
<font color="Maroon">C</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</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">r</font>,<font color="Maroon">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E20:102"/><b>then </b><i><font color="Green">E96</font></i>: 
<font color="Maroon">C</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font> is <a href="jct_misc.html#V1">connected</a>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E8:102"><i><font color="Green">E49</font></i></a></i>;<br/>
<a NAME="E21:102"/><i><font color="Green">E97</font></i>: 
not <font color="Maroon">C</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font> is <a href="xboole_0.html#V1">empty</a>
 
<b>by </b><i><a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="ref" href="rcomp_3.html#T30" target="_self">Th30</a>, <a class="ref" href="rcomp_3.html#T37" target="_self">Th37</a>, <a class="ref" href="rcomp_3.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E22:102"/><i><font color="Green">E98</font></i>: 
<font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</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">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> or <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">s</font> )
 </span><b>by </b><i><a class="ref" href="rcomp_3.html#T29" target="_self">Th29</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">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 ;<br/><div class="add"><a NAME="E2:102_1_1"/><b>then </b>
<font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">r</font></span><a href="rcomp_1.html#K1">.]</a></span></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T14" target="_self">Th14</a></i>;<br/><a NAME="E3:102_1_1"/><b>then </b><i><font color="Green">E99</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">C</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">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="ref" href="rcomp_3.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E5:102_1_1"/><b>then </b><i><font color="Green">E100</font></i>: 
( <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> &amp; <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">s</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">E101</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, <a class="ref" href="rcomp_3.html#T37" target="_self">Th37</a>, <a class="ref" href="rcomp_3.html#T30" target="_self">Th30</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</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_1.html#K1">.]</a></span></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, , <a class="ref" href="rcomp_3.html#T17" target="_self">Th17</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">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">n</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</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E91</font></i></a>, <a class="ref" href="rcomp_3.html#T42" target="_self">Th42</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">r</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">s</font>
 ;<br/><div class="add"><a NAME="E2:102_1_2"/><b>then </b>
<font color="Maroon">G</font> is <a href="seqm_3.html#V1">increasing</a>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T25" target="_self">Th25</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E3:102_1_2"/><b>then </b><i><font color="Green">E102</font></i>: 
<font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="rcomp_3.html#T34" target="_self">Th34</a>, <a class="ref" href="rcomp_3.html#T35" target="_self">Th35</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">E103</font></i>: 
2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="txt" href="rcomp_3.html#E23"><i><font color="Green">Lemma66</font></i></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">n</font> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> 2 ) or ( <font color="Maroon">n</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">G</font> ) or ( 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1 ) or ( 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</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">G</font> ) )
 </span><b>by </b><i><a class="ref" href="rcomp_3.html#T30" target="_self">Th30</a>, <a class="ref" href="rcomp_3.html#T32" target="_self">Th32</a>, <a class="ref" href="rcomp_3.html#T42" target="_self">Th42</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">E104</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E2:102_1_2_1_1"/><i><font color="Green">E105</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><a NAME="E3:102_1_2_1_1"/><i><font color="Green">E106</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> 2 <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="rcomp_3.html#T36" target="_self">Th36</a>, <a class="ref" href="rcomp_3.html#T43" target="_self">Th43</a></i>;<br/><a NAME="E4:102_1_2_1_1"/><b>then </b>
<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="ref" href="rcomp_3.html#T21" target="_self">Th21</a></i>;<br/><a NAME="E5:102_1_2_1_1"/><b>then </b><i><font color="Green">E107</font></i>: 
( <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> &amp; <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">s</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</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_1.html#K1">.]</a></span></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, , <a class="ref" href="rcomp_3.html#T17" target="_self">Th17</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">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">n</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</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E91</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">E108</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E2:102_1_2_1_2"/><i><font color="Green">E109</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">G</font>
 ;<br/><div class="add"><a NAME="E3:102_1_2_1_2"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">G</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</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</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="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="txt" href="rcomp_3.html#E22"><i><font color="Green">Lemma65</font></i></a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T43" target="_self">Th43</a></i>;<br/><a NAME="E4:102_1_2_1_2"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">r</font>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="txt" href="rcomp_3.html#E22"><i><font color="Green">Lemma65</font></i></a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E5:102_1_2_1_2"/><i><font color="Green">E112</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</font>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T43" target="_self">Th43</a>, <a class="ref" href="rcomp_3.html#T36" target="_self">Th36</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">E113</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="finseq_4.html#K4">/.</a> 1
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T19" target="_self">Th19</a></i>;<br/><a NAME="E7:102_1_2_1_2"/><i><font color="Green">E114</font></i>: 
<font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</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</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="ref" href="rcomp_3.html#T43" target="_self">Th43</a>, <a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E91</font></i></a>, <a class="ref" href="rcomp_3.html#T22" target="_self">Th22</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E8:102_1_2_1_2"/><i><font color="Green">E115</font></i>: 
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><font color="Maroon">C</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</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="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="txt" href="rcomp_3.html#E16:102"><i><font color="Green">E95</font></i></a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, <a class="ref" href="rcomp_3.html#T12" target="_self">Th12</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</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">G</font> <a href="seq_1.html#K2">.</a> 2
 <b>by </b><i>, <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</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E91</font></i></a>, <a class="txt" href="rcomp_3.html#E22:102"><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">G</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E21:102"><i><font color="Green">E97</font></i></a>, <a class="ref" href="rcomp_3.html#T38" target="_self">Th38</a>, <a class="ref" href="rcomp_3.html#T41" target="_self">Th41</a>, <a class="ref" href="rcomp_3.html#T40" target="_self">Th40</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">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">n</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</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E91</font></i></a>, , <a class="ref" href="rcomp_3.html#T38" target="_self">Th38</a>, <a class="txt" href="rcomp_3.html#E20:102"><i><font color="Green">E96</font></i></a>, <a class="ref" href="rcomp_3.html#T40" target="_self">Th40</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">E116</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E2:102_1_2_1_3"/><i><font color="Green">E117</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</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">E118</font></i>: 
<font color="Maroon">G</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">G</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="txt" href="rcomp_3.html#E22"><i><font color="Green">Lemma65</font></i></a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E4:102_1_2_1_3"/><i><font color="Green">E119</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T36" target="_self">Th36</a>, <a class="ref" href="rcomp_3.html#T43" target="_self">Th43</a></i>;<br/><a NAME="E5:102_1_2_1_3"/><b>then </b><i><font color="Green">E120</font></i>: 
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E91</font></i></a>, <a class="ref" href="rcomp_3.html#T23" target="_self">Th23</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E6:102_1_2_1_3"/><i><font color="Green">E121</font></i>: 
1 <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="txt" href="rcomp_3.html#E14:102"><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">E122</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</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">E123</font></i>: 
<font color="Maroon">n</font> <a href="xcmplx_0.html#K6">-</a> 1 is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="txt" href="rcomp_3.html#E20:102"><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">G</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">n</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</font> <a href="finseq_4.html#K4">/.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">n</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</font> <a href="finseq_4.html#K4">/.</a> <span class="p4">(<span class="default"><font color="Maroon">n</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="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="txt" href="rcomp_3.html#E21:102"><i><font color="Green">E97</font></i></a>, <a class="ref" href="rcomp_3.html#T43" target="_self">Th43</a>, , <a class="txt" href="rcomp_3.html#E22"><i><font color="Green">Lemma65</font></i></a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E10:102_1_2_1_3"/><b>then </b><i><font color="Green">E124</font></i>: 
<font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</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</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">n</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</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><font color="Maroon">n</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</font> <a href="finseq_4.html#K4">/.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">n</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="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, , <a class="txt" href="rcomp_3.html#E22:102"><i><font color="Green">E98</font></i></a>, <a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="txt" href="rcomp_3.html#E21:102"><i><font color="Green">E97</font></i></a>, <a class="ref" href="rcomp_3.html#T12" target="_self">Th12</a></i>;<br/><a NAME="E12:102_1_2_1_3"/><b>then </b>
<font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</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</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i>, <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">E125</font></i>: 
<font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="txt" href="rcomp_3.html#E16:102"><i><font color="Green">E95</font></i></a>, <a class="ref" href="rcomp_3.html#T38" target="_self">Th38</a>, <a class="ref" href="rcomp_3.html#T41" target="_self">Th41</a>, <a class="ref" href="rcomp_3.html#T40" target="_self">Th40</a>, </i>;<br/><a NAME="E14:102_1_2_1_3"/>
<font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T36" target="_self">Th36</a>, <a class="ref" href="rcomp_3.html#T38" target="_self">Th38</a>, <a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a>, , , <a class="ref" href="rcomp_3.html#T20" target="_self">Th20</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">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">n</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</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="rcomp_3.html#T38" target="_self">Th38</a>, <a class="ref" href="rcomp_3.html#T40" target="_self">Th40</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">E126</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E2:102_1_2_1_4"/><i><font color="Green">E160</font></i>: 
<font color="Maroon">n</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">G</font>
 ;<br/><div class="add"><a NAME="E3:102_1_2_1_4"/>
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T31" target="_self">Th31</a>, <a class="ref" href="rcomp_3.html#T36" target="_self">Th36</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">E161</font></i>: 
 <a href="pscomp_1.html#K3">inf</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="txt" href="rcomp_3.html#E14:102"><i><font color="Green">E91</font></i></a>, <a class="ref" href="rcomp_3.html#T23" target="_self">Th23</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E5:102_1_2_1_4"/><i><font color="Green">E162</font></i>: 
<font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</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</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T26" target="_self">Th26</a>, <a class="ref" href="rcomp_3.html#T27" target="_self">Th27</a>, <a class="ref" href="rcomp_3.html#T29" target="_self">Th29</a>, <a class="ref" href="rcomp_3.html#T30" target="_self">Th30</a>, <a class="ref" href="rcomp_3.html#T43" target="_self">Th43</a>, <a class="ref" href="rcomp_3.html#T22" target="_self">Th22</a>, <a class="ref" href="rcomp_3.html#T28" target="_self">Th28</a></i>;<br/><a NAME="E6:102_1_2_1_4"/><b>then </b>
<font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</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</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i>, <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">E163</font></i>: 
<font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="rcomp_3.html#T38" target="_self">Th38</a>, <a class="ref" href="rcomp_3.html#T41" target="_self">Th41</a>, <a class="ref" href="rcomp_3.html#T40" target="_self">Th40</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</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">n</font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
 <b>by </b><i>, , <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">G</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="rcomp_3.html#T38" target="_self">Th38</a>, <a class="ref" href="rcomp_3.html#T41" target="_self">Th41</a>, <a class="ref" href="rcomp_3.html#T40" target="_self">Th40</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">G</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="seq_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">n</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</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="rcomp_3.html#T38" target="_self">Th38</a>, <a class="txt" href="rcomp_3.html#E16:102"><i><font color="Green">E95</font></i></a>, <a class="ref" href="rcomp_3.html#T40" target="_self">Th40</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>
