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

<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>thus </b><a NAME="E1:86"/>
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> implies  <a href="pscomp_1.html#K6">Cl</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:86_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">a1</font> = <font color="Maroon">a</font>, <font color="Maroon">b1</font> = <font color="Maroon">b</font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:86_1_1"/>
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> )
 </span><b>by </b><i>, <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="86_1_1_1"><b>suppose </b></a><a NAME="E1:86_1_1_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><b>hence </b> <a href="pscomp_1.html#K6">Cl</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="pscomp_1.html#T35">PSCOMP_1:35</a>, <a class="ref" href="rcomp_1.html#T12">RCOMP_1:12</a></i>
<br/>.= 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span>
<b>by </b><i>, <a class="ref" href="rcomp_1.html#T13">RCOMP_1:13</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_2"><b>suppose </b></a><a NAME="E1:86_1_1_2"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><a NAME="E2:86_1_1_2"/>
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i><a class="ref" href="rcomp_1.html#T15">RCOMP_1:15</a></i>;<br/><b>hence </b><a NAME="E3:86_1_1_2"/>
 <a href="pscomp_1.html#K6">Cl</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T32">PSCOMP_1:32</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/><a NAME="E4:86_1_1_2"/><i><font color="Green">E59</font></i>: 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">w</font> &amp; <font color="Olive">w</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="rcomp_1.html#D1">RCOMP_1:def 1</a></i>;<br/><a NAME="E5:86_1_1_2"/><i><font color="Green">E66</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">w</font> &amp; <font color="Olive">w</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="rcomp_1.html#D2">RCOMP_1:def 2</a></i>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/><b>assume </b><a NAME="E6:86_1_1_2"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span>
 ;<br/><b>then consider </b><font color="Maroon">r</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E8:86_1_1_2"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E9:86_1_1_2"/><i><font color="Green">E69</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> &amp; <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> )
 <b>by </b><i/>;<br/><a NAME="E10:86_1_1_2"/>
( <font color="Maroon">a1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> 2 &amp; <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b1</font> )
 <b>by </b><i>, <a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/><a NAME="E11:86_1_1_2"/><b>then </b><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">b1</font></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i/>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:86_1_1_2_1_1"/>
( ( <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">r</font> &amp; <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> ) or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> or <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> )
 </span><b>by </b><i>, <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="86_1_1_2_1_1_1"><b>case </b></a><a NAME="E1:86_1_1_2_1_1_1"/>
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">r</font> &amp; <font color="Maroon">r</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:86_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i/>;<br/><a NAME="E3:86_1_1_2_1_1_1"/>
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a>  <a href="pscomp_1.html#K6">Cl</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T33">PSCOMP_1:33</a></i>;<br/><b>hence </b><a NAME="E4:86_1_1_2_1_1_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K6">Cl</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_2_1_1_2"><b>case </b></a><a NAME="E1:86_1_1_2_1_1_2"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font>
 ;<br/><div class="add"><a NAME="E2:86_1_1_2_1_1_2"/>
for <font color="Olive">O</font> being <a href="rcomp_1.html#V3">open</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>   st <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Olive">O</font> holds <br/> not <font color="Olive">O</font> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> is <a href="xboole_0.html#V1">empty</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1_1_2_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">O</font> be  <a href="rcomp_1.html#V3">open</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:86_1_1_2_1_1_2_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font>
 ;<br/>

<b>then consider </b><font color="Maroon">g</font> being  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E3:86_1_1_2_1_1_2_1"/><i><font color="Green">E83</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E4:86_1_1_2_1_1_2_1"/><i><font color="Green">E84</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">O</font>
 <b>by </b><i><a class="ref" href="rcomp_1.html#T40">RCOMP_1:40</a></i>;<br/>
<b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">g</font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<a NAME="E6:86_1_1_2_1_1_2_1"/><i><font color="Green">E85</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">w</font> &amp; <font color="Olive">w</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="rcomp_1.html#D2">RCOMP_1:def 2</a></i>;<br/>
<a NAME="E7:86_1_1_2_1_1_2_1"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> 0
 
<b>by </b><i>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_2_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:86_1_1_2_1_1_2_1_1"/>
( <font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> or <font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">b</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_2_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:86_1_1_2_1_1_2_1_1_1"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><a NAME="E2:86_1_1_2_1_1_2_1_1_1"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:86_1_1_2_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E89</font></i>: 
<font color="Maroon">a1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i><a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/><a NAME="E4:86_1_1_2_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E90</font></i>: 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="topreal6.html#E1"><i><font color="Green">Lemma54</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:86_1_1_2_1_1_2_1_1_1"/><i><font color="Green">E91</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="txt" href="topreal6.html#E1:86_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/><a NAME="E6:86_1_1_2_1_1_2_1_1_1"/><b>then </b><i><font color="Green">E92</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2 <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"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">g</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, <a class="txt" href="topreal6.html#E1:86_1_1_2"><i><font color="Green">E58</font></i></a></i>;<br/><a NAME="E7:86_1_1_2_1_1_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="topreal6.html#T6" target="_self">Th6</a>, <a class="txt" href="topreal6.html#E4:86_1_1_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E8:86_1_1_2_1_1_2_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">b1</font></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E9:86_1_1_2_1_1_2_1_1_1"/>
not <font color="Maroon">O</font> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i>, <a class="ref" href="topreal6.html#T7" target="_self">Th7</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_2_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:86_1_1_2_1_1_2_1_1_2"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><a NAME="E2:86_1_1_2_1_1_2_1_1_2"/>
<font color="Maroon">a1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i>, <a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/><a NAME="E3:86_1_1_2_1_1_2_1_1_2"/><b>then </b><i><font color="Green">E94</font></i>: 
<font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="topreal6.html#E1"><i><font color="Green">Lemma54</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:86_1_1_2_1_1_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b1</font>
 <b>by </b><i>, <a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/><a NAME="E5:86_1_1_2_1_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="topreal6.html#T6" target="_self">Th6</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E6:86_1_1_2_1_1_2_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> 2 <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"><font color="Maroon">a1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">g</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, <a class="txt" href="topreal6.html#E1:86_1"><i><font color="Green">E56</font></i></a></i>;<br/><b>hence </b><a NAME="E7:86_1_1_2_1_1_2_1_1_2"/>
not <font color="Maroon">O</font> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E3:86_1_1_2_1_1_2"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K6">Cl</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, , <a class="ref" href="pscomp_1.html#T38">PSCOMP_1:38</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_2_1_1_3"><b>case </b></a><a NAME="E1:86_1_1_2_1_1_3"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font>
 ;<br/><div class="add"><a NAME="E2:86_1_1_2_1_1_3"/>
for <font color="Olive">O</font> being <a href="rcomp_1.html#V3">open</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>   st <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Olive">O</font> holds <br/> not <font color="Olive">O</font> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> is <a href="xboole_0.html#V1">empty</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1_1_2_1_1_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">O</font> be  <a href="rcomp_1.html#V3">open</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><a NAME="E1:86_1_1_2_1_1_3_1"/>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">O</font>
 ;<br/>

<b>then consider </b><font color="Maroon">g</font> being  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> <b> such that </b><br/><a NAME="E3:86_1_1_2_1_1_3_1"/><i><font color="Green">E96</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E4:86_1_1_2_1_1_3_1"/><i><font color="Green">E97</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">O</font>
 <b>by </b><i><a class="ref" href="rcomp_1.html#T40">RCOMP_1:40</a></i>;<br/>
<b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">g</font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<a NAME="E6:86_1_1_2_1_1_3_1"/><i><font color="Green">E98</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is   <a href="real_1.html#NM1">Real</a> : ( <font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">w</font> &amp; <font color="Olive">w</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="rcomp_1.html#D2">RCOMP_1:def 2</a></i>;<br/>
<a NAME="E7:86_1_1_2_1_1_3_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> 0
 
<b>by </b><i>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/>
<a NAME="E8:86_1_1_2_1_1_3_1"/><i><font color="Green">E147</font></i>: 
<font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font>
 
<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="86_1_1_2_1_1_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:86_1_1_2_1_1_3_1_1"/>
( <font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">a</font> or <font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_2_1_1_3_1_1_1"><b>suppose </b></a><a NAME="E1:86_1_1_2_1_1_3_1_1_1"/><i><font color="Green">E148</font></i>: 
<font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><a NAME="E2:86_1_1_2_1_1_3_1_1_1"/><i><font color="Green">E149</font></i>: 
<font color="Maroon">b1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i><a class="txt" href="topreal6.html#E1"><i><font color="Green">Lemma54</font></i></a>, <a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/><a NAME="E3:86_1_1_2_1_1_3_1_1_1"/><b>then </b><i><font color="Green">E150</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="topreal6.html#E1:86_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:86_1_1_2_1_1_3_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b1</font>
 <b>by </b><i><a class="txt" href="topreal6.html#E1"><i><font color="Green">Lemma54</font></i></a>, <a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/><a NAME="E5:86_1_1_2_1_1_3_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="topreal6.html#T6" target="_self">Th6</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E6:86_1_1_2_1_1_3_1_1_1"/><b>then </b><i><font color="Green">E151</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2 <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"><font color="Maroon">b1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">g</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, </i>;<br/><a NAME="E7:86_1_1_2_1_1_3_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b1</font>
 <b>by </b><i><a class="txt" href="topreal6.html#E1"><i><font color="Green">Lemma54</font></i></a>, <a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/><a NAME="E8:86_1_1_2_1_1_3_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">b1</font></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, <a class="txt" href="topreal6.html#E1:86_1_1_2"><i><font color="Green">E58</font></i></a></i>;<br/><b>hence </b><a NAME="E9:86_1_1_2_1_1_3_1_1_1"/>
not <font color="Maroon">O</font> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i>, <a class="txt" href="topreal6.html#E4:86_1_1_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="86_1_1_2_1_1_3_1_1_2"><b>suppose </b></a><a NAME="E1:86_1_1_2_1_1_3_1_1_2"/><i><font color="Green">E152</font></i>: 
<font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><a NAME="E2:86_1_1_2_1_1_3_1_1_2"/>
<font color="Maroon">a1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i>, <a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/><a NAME="E3:86_1_1_2_1_1_3_1_1_2"/><b>then </b><i><font color="Green">E153</font></i>: 
<font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">g</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="topreal6.html#E1:86_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E4:86_1_1_2_1_1_3_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b1</font>
 <b>by </b><i>, <a class="ref" href="topreal3.html#T3">TOPREAL3:3</a></i>;<br/><a NAME="E5:86_1_1_2_1_1_3_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="topreal6.html#T6" target="_self">Th6</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E6:86_1_1_2_1_1_3_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">b1</font></span>)</span> <a href="real_1.html#K6">/</a> 2 <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"><font color="Maroon">b1</font> <a href="real_1.html#K5">-</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="real_1.html#K3">+</a> <font color="Maroon">g</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E7:86_1_1_2_1_1_3_1_1_2"/>
not <font color="Maroon">O</font> <a href="subset_1.html#K9">/\</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>hence </b><a NAME="E3:86_1_1_2_1_1_3"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K6">Cl</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, , <a class="ref" href="pscomp_1.html#T38">PSCOMP_1:38</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E13:86_1_1_2"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K6">Cl</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>

<b>assume </b><b>that </b><br/><a NAME="E2:86"/><i><font color="Green">E154</font></i>: 
 <a href="pscomp_1.html#K6">Cl</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>and </b><br/><a NAME="E3:86"/><i><font color="Green">E155</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E4:86"/>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="rcomp_1.html#T14">RCOMP_1:14</a></i>;<br/>
<b>hence </b><a NAME="E5:86"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="pscomp_1.html#T35">PSCOMP_1:35</a>, <a class="ref" href="rcomp_1.html#T12">RCOMP_1:12</a></i>;<br/>


</div>
