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

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="supinf_1.html#NM3">R_eal</a>] means ( ex <font color="Olive">b<sub>1</sub></font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st <br/>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>2</sub></font> holds <br/>ex <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>for <font color="Olive">b<sub>4</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>4</sub></font> holds <br/><span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>2</sub></font> ) &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V7" target="_self">convergent_to_finite_number</a> ) or ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K1">+infty</a>  &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V8" target="_self">convergent_to_+infty</a> ) or ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K2">-infty</a>  &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V9" target="_self">convergent_to_-infty</a> ) );<br/>
<b>given </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="supinf_1.html#NM3">R_eal</a><b> such that </b><a NAME="E1:77_1_2"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>]
 <b>and </b><br/><a NAME="E2:77_1_2"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>3</sub></font>]
 <b>and </b><br/><a NAME="E3:77_1_2"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="77_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:77_1_2_1"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V7" target="_self">convergent_to_finite_number</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V8" target="_self">convergent_to_+infty</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V9" target="_self">convergent_to_-infty</a> )
 </span><b>by </b><i><a class="txt" href="mesfunc5.html#E1:77"><i><font color="Green">E72</font></i></a>, <a class="ref" href="mesfunc5.html#D11" target="_self">Def11</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="77_1_2_1_1"><b>suppose </b></a><a NAME="E1:77_1_2_1_1"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V7" target="_self">convergent_to_finite_number</a>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>4</sub></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="E3:77_1_2_1_1"/><i><font color="Green">E77</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>3</sub></font> holds <br/><span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> ) &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V7" target="_self">convergent_to_finite_number</a> )
 <b>by </b><i><a class="ref" href="mesfunc5.html#T56" target="_self">Th56</a>, <a class="ref" href="mesfunc5.html#T57" target="_self">Th57</a>, <a class="txt" href="mesfunc5.html#E1:77_1_2"><i><font color="Green">E73</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></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="E5:77_1_2_1_1"/><i><font color="Green">E78</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> holds <br/>ex <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>3</sub></font> holds <br/><span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> ) &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V7" target="_self">convergent_to_finite_number</a> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E1:77_1_2_1_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="mesfunc5.html#T56" target="_self">Th56</a>, <a class="ref" href="mesfunc5.html#T57" target="_self">Th57</a>, <a class="txt" href="mesfunc5.html#E2:77_1_2"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E6:77_1_2_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="mesfunc5.html#E3:77_1_2"><i><font color="Green">E75</font></i></a>, <a class="txt" href="mesfunc5.html#E3:77_1_2_1_1"><i><font color="Green">E77</font></i></a>, <a class="txt" href="mesfunc5.html#E5:77_1_2_1_1"><i><font color="Green">E78</font></i></a></i>;<br/><a NAME="E7:77_1_2_1_1"/><b>then </b>
<span class="p1"><a href="complex1.html#K16">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="complex1.html#T133">COMPLEX1:133</a></i>;<br/><a NAME="E8:77_1_2_1_1"/><b>then </b><i><font color="Green">E79</font></i>: 
<span class="p1"><a href="complex1.html#K16">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T141">XREAL_1:141</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:77_1_2_1_1"/><i><font color="Green">E80</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="measure6.html#K1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E3:77_1_2_1_1"><i><font color="Green">E77</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E12:77_1_2_1_1"/><i><font color="Green">E81</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="measure6.html#K1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E5:77_1_2_1_1"><i><font color="Green">E78</font></i></a>, <a class="txt" href="mesfunc5.html#E8:77_1_2_1_1"><i><font color="Green">E79</font></i></a></i>;<br/><b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/><a NAME="E13:77_1_2_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="ref" href="square_1.html#T46">SQUARE_1:46</a></i>;<br/><a NAME="E14:77_1_2_1_1"/><b>then </b><i><font color="Green">E82</font></i>: 
( <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="measure6.html#K1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> &amp; <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="measure6.html#K1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E10:77_1_2_1_1"><i><font color="Green">E80</font></i></a>, <a class="txt" href="mesfunc5.html#E12:77_1_2_1_1"><i><font color="Green">E81</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>5</sub></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="E16:77_1_2_1_1"/><i><font color="Green">E83</font></i>: 
<span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="extreal2.html#T15">EXTREAL2:15</a></i>;<br/><a NAME="E17:77_1_2_1_1"/><b>then </b>
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p5">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="measure6.html#K1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E14:77_1_2_1_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="extreal2.html#T66">EXTREAL2:66</a></i>;<br/><a NAME="E18:77_1_2_1_1"/><b>then </b><i><font color="Green">E84</font></i>: 
(  <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="measure6.html#K1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> &amp;  <a href="supinf_2.html#K3">-</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="measure6.html#K1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E14:77_1_2_1_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="extreal2.html#T58">EXTREAL2:58</a></i>;<br/><a NAME="E19:77_1_2_1_1"/><b>then </b><i><font color="Green">E85</font></i>: 
( <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a>  )
 <b>by </b><i><a class="ref" href="measure5.html#T16">MEASURE5:16</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="txt" href="mesfunc5.html#E18:77_1_2_1_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="measure5.html#T16">MEASURE5:16</a></i>;<br/><a NAME="E21:77_1_2_1_1"/><i><font color="Green">E86</font></i>: 
<span class="p1"><a href="complex1.html#K16">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2 <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a> 
 <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/><a NAME="E22:77_1_2_1_1"/>
<span class="p1"><a href="complex1.html#K16">|.</a><span class="default"><font color="Maroon">c<sub>11</sub></font></span><a href="complex1.html#K16">.|</a></span> <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a> 
 <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/><a NAME="E23:77_1_2_1_1"/><b>then </b>
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="hidden.html#R2">in</a>  <a href="supinf_1.html#K3">REAL</a> 
 <b>by </b><i><a class="ref" href="extreal2.html#T49">EXTREAL2:49</a></i>;<br/><a NAME="E24:77_1_2_1_1"/><b>then </b>
( <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="supinf_2.html#K2">+</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> &amp; <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E14:77_1_2_1_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="mesfunc5.html#E21:77_1_2_1_1"><i><font color="Green">E86</font></i></a>, <a class="ref" href="measure6.html#T12">MEASURE6:12</a></i>;<br/><a NAME="E25:77_1_2_1_1"/><b>then </b><i><font color="Green">E87</font></i>: 
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="supinf_2.html#K2">+</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="supinf_1.html#T29">SUPINF_1:29</a></i>;<br/><a NAME="E26:77_1_2_1_1"/><i><font color="Green">E88</font></i>: 
( <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K1">+infty</a>  &amp; <span class="p1">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K2">-infty</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K1">+infty</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K2">-infty</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="supinf_1.html#K1">+infty</a>  &amp;  <a href="supinf_1.html#K2">-infty</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E19:77_1_2_1_1"><i><font color="Green">E85</font></i></a>, <a class="ref" href="supinf_1.html#T31">SUPINF_1:31</a></i>;<br/><a NAME="E27:77_1_2_1_1"/><b>then </b><i><font color="Green">E89</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K1">+infty</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="supinf_1.html#K2">-infty</a>  )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E5:77_1_2_1_1"><i><font color="Green">E78</font></i></a>, <a class="ref" href="extreal2.html#T25">EXTREAL2:25</a>, <a class="ref" href="extreal2.html#T26">EXTREAL2:26</a></i>;<br/><span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> = 
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="supinf_2.html#K2">+</a> <span class="p4">(<span class="default"><a href="measure6.html#K1">R_EAL</a> 0</span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span>
<b>by </b><i><a class="ref" href="supinf_2.html#T18">SUPINF_2:18</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="supinf_2.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p0">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p5">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span>
<b>by </b><i><a class="ref" href="extreal1.html#T9">EXTREAL1:9</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p5">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span>
<b>by </b><i><a class="txt" href="mesfunc5.html#E3:77_1_2_1_1"><i><font color="Green">E77</font></i></a>, <a class="txt" href="mesfunc5.html#E27:77_1_2_1_1"><i><font color="Green">E89</font></i></a>, <a class="ref" href="extreal1.html#T8">EXTREAL1:8</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p0">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p5">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span><a href="extreal1.html#K4">.|</a></span>
<b>by </b><i><a class="txt" href="mesfunc5.html#E5:77_1_2_1_1"><i><font color="Green">E78</font></i></a>, <a class="txt" href="mesfunc5.html#E26:77_1_2_1_1"><i><font color="Green">E88</font></i></a>, <a class="ref" href="extreal1.html#T11">EXTREAL1:11</a></i>
;<br/><a NAME="E29:77_1_2_1_1"/><b>then </b>
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="supinf_2.html#K3">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p5">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="supinf_2.html#K2">+</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E26:77_1_2_1_1"><i><font color="Green">E88</font></i></a>, <a class="ref" href="extreal2.html#T61">EXTREAL2:61</a></i>;<br/><a NAME="E30:77_1_2_1_1"/><b>then </b><i><font color="Green">E90</font></i>: 
<span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span> <a href="supinf_2.html#K2">+</a> <span class="p1"><a href="extreal1.html#K4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="mesfunc1.html#K4">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1">max</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="extreal1.html#K4">.|</a></span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E16:77_1_2_1_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="extreal2.html#T66">EXTREAL2:66</a></i>;<br/><a NAME="E31:77_1_2_1_1"/><i><font color="Green">E91</font></i>: 
<span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="supinf_2.html#K2">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="complex1.html#K16">.|</a></span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="mesfunc5.html#T7" target="_self">Th7</a></i>;<br/><a NAME="E32:77_1_2_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E3:77_1_2_1_1"><i><font color="Green">E77</font></i></a>, <a class="txt" href="mesfunc5.html#E5:77_1_2_1_1"><i><font color="Green">E78</font></i></a>, <a class="ref" href="supinf_2.html#T5">SUPINF_2:5</a></i>;<br/><b>hence </b><a NAME="E33:77_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="mesfunc5.html#E25:77_1_2_1_1"><i><font color="Green">E87</font></i></a>, <a class="txt" href="mesfunc5.html#E30:77_1_2_1_1"><i><font color="Green">E90</font></i></a>, <a class="txt" href="mesfunc5.html#E31:77_1_2_1_1"><i><font color="Green">E91</font></i></a>, <a class="ref" href="extreal2.html#T49">EXTREAL2:49</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="77_1_2_1_2"><b>suppose </b></a><a NAME="E1:77_1_2_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V8" target="_self">convergent_to_+infty</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="mesfunc5.html#V9" target="_self">convergent_to_-infty</a> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:77_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="mesfunc5.html#E1:77_1_2"><i><font color="Green">E73</font></i></a>, <a class="txt" href="mesfunc5.html#E2:77_1_2"><i><font color="Green">E74</font></i></a>, <a class="txt" href="mesfunc5.html#E3:77_1_2"><i><font color="Green">E75</font></i></a>, <a class="ref" href="mesfunc5.html#T56" target="_self">Th56</a>, <a class="ref" href="mesfunc5.html#T57" target="_self">Th57</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
