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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a>] <b>means </b>(  ex <font color="Olive" title="b1">g</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  st <br/>( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> &amp; ( for <font color="Olive" title="b2">p</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b2">p</font> holds <br/> ex <font color="Olive" title="b3">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>for <font color="Olive" title="b4">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b3">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">m</font> holds <br/><span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="supinf_2.html#K15" title="SUPINF_2:func.15">.</a> <font color="Olive" title="b4">m</font></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> $1</span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">p</font> ) &amp; <font color="Maroon" title="c1">seq</font> is <a href="mesfunc5.html#V7" title="MESFUNC5:attr.7">convergent_to_finite_number</a> ) or ( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  &amp; <font color="Maroon" title="c1">seq</font> is <a href="mesfunc5.html#V8" title="MESFUNC5:attr.8">convergent_to_+infty</a> ) or ( $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_1.html#K2" title="SUPINF_1:func.2">-infty</a>  &amp; <font color="Maroon" title="c1">seq</font> is <a href="mesfunc5.html#V9" title="MESFUNC5:attr.9">convergent_to_-infty</a> ) );<br/>
<b>given </b><font color="Maroon" title="c2">g1</font>, <font color="Maroon" title="c3">g2</font> being   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a><b> such that </b><a NAME="E2:77_1_2"/><i><font color="Green" title="E73">A3</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">g1</font>]
 <b>and </b><br/><a NAME="E3:77_1_2"/><i><font color="Green" title="E74">A4</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">g2</font>]
 <b>and </b><br/><a NAME="E4:77_1_2"/><i><font color="Green" title="E75">A5</font></i>: 
<font color="Maroon" title="c2">g1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">g2</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" title="c1">seq</font> is <a href="mesfunc5.html#V7" title="MESFUNC5:attr.7">convergent_to_finite_number</a> or <font color="Maroon" title="c1">seq</font> is <a href="mesfunc5.html#V8" title="MESFUNC5:attr.8">convergent_to_+infty</a> or <font color="Maroon" title="c1">seq</font> is <a href="mesfunc5.html#V9" title="MESFUNC5:attr.9">convergent_to_-infty</a> )
 </span><b>by </b><i><a class="txt" href="mesfunc5.html#E1:77"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="mesfunc5.html#D11" target="_self" title="MESFUNC5:def.11">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" title="E76">A6</font></i>: 
<font color="Maroon" title="c1">seq</font> is <a href="mesfunc5.html#V7" title="MESFUNC5:attr.7">convergent_to_finite_number</a>
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">g</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E3:77_1_2_1_1"/><i><font color="Green" title="E77">A7</font></i>: 
( <font color="Maroon" title="c2">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> &amp; ( for <font color="Olive" title="b1">p</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">p</font> holds <br/> ex <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>for <font color="Olive" title="b3">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">m</font> holds <br/><span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="supinf_2.html#K15" title="SUPINF_2:func.15">.</a> <font color="Olive" title="b3">m</font></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c2">g1</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">p</font> ) &amp; <font color="Maroon" title="c1">seq</font> is <a href="mesfunc5.html#V7" title="MESFUNC5:attr.7">convergent_to_finite_number</a> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E2:77_1_2"><i><font color="Green" title="E73">A3</font></i></a>, <a class="ref" href="mesfunc5.html#T56" target="_self" title="MESFUNC5:th.56">Th56</a>, <a class="ref" href="mesfunc5.html#T57" target="_self" title="MESFUNC5:th.57">Th57</a></i>;<br/><b>consider </b><font color="Maroon" title="c5">h</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E5:77_1_2_1_1"/><i><font color="Green" title="E78">A8</font></i>: 
( <font color="Maroon" title="c3">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">h</font> &amp; ( for <font color="Olive" title="b1">p</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">p</font> holds <br/> ex <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>for <font color="Olive" title="b3">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">m</font> holds <br/><span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="supinf_2.html#K15" title="SUPINF_2:func.15">.</a> <font color="Olive" title="b3">m</font></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">p</font> ) &amp; <font color="Maroon" title="c1">seq</font> is <a href="mesfunc5.html#V7" title="MESFUNC5:attr.7">convergent_to_finite_number</a> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E3:77_1_2"><i><font color="Green" title="E74">A4</font></i></a>, <a class="txt" href="mesfunc5.html#E1:77_1_2_1_1"><i><font color="Green" title="E76">A6</font></i></a>, <a class="ref" href="mesfunc5.html#T56" target="_self" title="MESFUNC5:th.56">Th56</a>, <a class="ref" href="mesfunc5.html#T57" target="_self" title="MESFUNC5:th.57">Th57</a></i>;<br/><a NAME="E6:77_1_2_1_1"/>
<font color="Maroon" title="c4">g</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">h</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="mesfunc5.html#E4:77_1_2"><i><font color="Green" title="E75">A5</font></i></a>, <a class="txt" href="mesfunc5.html#E3:77_1_2_1_1"><i><font color="Green" title="E77">A7</font></i></a>, <a class="txt" href="mesfunc5.html#E5:77_1_2_1_1"><i><font color="Green" title="E78">A8</font></i></a></i>;<br/><a NAME="E7:77_1_2_1_1"/><b>then </b>
<span class="p1"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="complex1.html#T133" title="COMPLEX1:th.133">COMPLEX1:133</a></i>;<br/><a NAME="E8:77_1_2_1_1"/><b>then </b><i><font color="Green" title="E79">A9</font></i>: 
<span class="p1"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T141" title="XREAL_1:th.141">XREAL_1:141</a></i>;<br/><b>then consider </b><font color="Maroon" title="c6">n1</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E10:77_1_2_1_1"/><i><font color="Green" title="E80">A10</font></i>: 
for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon" title="c6">n1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">m</font> holds <br/><span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="supinf_2.html#K15" title="SUPINF_2:func.15">.</a> <font color="Olive" title="b1">m</font></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c2">g1</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E3:77_1_2_1_1"><i><font color="Green" title="E77">A7</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c7">n2</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E12:77_1_2_1_1"/><i><font color="Green" title="E81">A11</font></i>: 
for <font color="Olive" title="b1">m</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon" title="c7">n2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">m</font> holds <br/><span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="supinf_2.html#K15" title="SUPINF_2:func.15">.</a> <font color="Olive" title="b1">m</font></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E5:77_1_2_1_1"><i><font color="Green" title="E78">A8</font></i></a>, <a class="txt" href="mesfunc5.html#E8:77_1_2_1_1"><i><font color="Green" title="E79">A9</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">n1</font> = <font color="Maroon" title="c6">n1</font>, <font color="Maroon" title="c9">n2</font> = <font color="Maroon" title="c7">n2</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><b>set </b><font color="Maroon" title="c10">m</font> =  <a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font>;<br/><a NAME="E14:77_1_2_1_1"/>
( <font color="Maroon" title="c8">n1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font> &amp; <font color="Maroon" title="c9">n2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font> )
 <b>by </b><i><a class="ref" href="xxreal_0.html#T25" title="XXREAL_0:th.25">XXREAL_0:25</a></i>;<br/><a NAME="E15:77_1_2_1_1"/><b>then </b><i><font color="Green" title="E82">A12</font></i>: 
( <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c2">g1</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span> &amp; <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c5">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E10:77_1_2_1_1"><i><font color="Green" title="E80">A10</font></i></a>, <a class="txt" href="mesfunc5.html#E12:77_1_2_1_1"><i><font color="Green" title="E81">A11</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">g</font> = <font color="Maroon" title="c4">g</font>, <font color="Maroon" title="c12">h</font> = <font color="Maroon" title="c5">h</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/><a NAME="E17:77_1_2_1_1"/><i><font color="Green" title="E83">A13</font></i>: 
<span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c2">g1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c2">g1</font></span>)</span>
 <b>by </b><i><a class="ref" href="extreal2.html#T15" title="EXTREAL2:th.15">EXTREAL2:15</a></i>;<br/><a NAME="E18:77_1_2_1_1"/><b>then </b>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p5">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c2">g1</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E15:77_1_2_1_1"><i><font color="Green" title="E82">A12</font></i></a>, <a class="ref" href="extreal2.html#T66" title="EXTREAL2:th.66">EXTREAL2:66</a></i>;<br/><a NAME="E19:77_1_2_1_1"/><b>then </b><i><font color="Green" title="E84">A14</font></i>: 
(  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c2">g1</font> &amp; <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c2">g1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span> &amp;  <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E15:77_1_2_1_1"><i><font color="Green" title="E82">A12</font></i></a>, <a class="ref" href="extreal2.html#T58" title="EXTREAL2:th.58">EXTREAL2:58</a></i>;<br/><a NAME="E20:77_1_2_1_1"/><b>then </b><i><font color="Green" title="E85">A15</font></i>: 
( <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c2">g1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a>  )
 <b>by </b><i><a class="ref" href="measure5.html#T16" title="MEASURE5:th.16">MEASURE5:16</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">w</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="txt" href="mesfunc5.html#E19:77_1_2_1_1"><i><font color="Green" title="E84">A14</font></i></a>, <a class="ref" href="measure5.html#T16" title="MEASURE5:th.16">MEASURE5:16</a></i>;<br/><a NAME="E22:77_1_2_1_1"/><i><font color="Green" title="E86">A16</font></i>: 
<span class="p1"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> 
 <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/><a NAME="E23:77_1_2_1_1"/>
<span class="p1"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><font color="Maroon" title="c13">w</font></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> 
 <b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/><a NAME="E24:77_1_2_1_1"/><b>then </b>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> 
 <b>by </b><i><a class="ref" href="extreal2.html#T49" title="EXTREAL2:th.49">EXTREAL2:49</a></i>;<br/><a NAME="E25:77_1_2_1_1"/><b>then </b>
( <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c2">g1</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> &amp; <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E15:77_1_2_1_1"><i><font color="Green" title="E82">A12</font></i></a>, <a class="txt" href="mesfunc5.html#E22:77_1_2_1_1"><i><font color="Green" title="E86">A16</font></i></a>, <a class="ref" href="measure6.html#T12" title="MEASURE6:th.12">MEASURE6:12</a></i>;<br/><a NAME="E26:77_1_2_1_1"/><b>then </b><i><font color="Green" title="E87">A17</font></i>: 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c2">g1</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E27:77_1_2_1_1"/><i><font color="Green" title="E88">A18</font></i>: 
( <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c2">g1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  &amp; <span class="p1">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p3">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c2">g1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K2" title="SUPINF_1:func.2">-infty</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K2" title="SUPINF_1:func.2">-infty</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  &amp;  <a href="supinf_1.html#K2" title="SUPINF_1:func.2">-infty</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p2">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font> )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E20:77_1_2_1_1"><i><font color="Green" title="E85">A15</font></i></a>, <a class="ref" href="xxreal_0.html#T9" title="XXREAL_0:th.9">XXREAL_0:9</a>, <a class="ref" href="xxreal_0.html#T12" title="XXREAL_0:th.12">XXREAL_0:12</a></i>;<br/><a NAME="E28:77_1_2_1_1"/><b>then </b><i><font color="Green" title="E89">A19</font></i>: 
( <font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  &amp; <font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="supinf_1.html#K2" title="SUPINF_1:func.2">-infty</a>  )
 <b>by </b><i><a class="txt" href="mesfunc5.html#E5:77_1_2_1_1"><i><font color="Green" title="E78">A8</font></i></a>, <a class="ref" href="extreal2.html#T25" title="EXTREAL2:th.25">EXTREAL2:25</a>, <a class="ref" href="extreal2.html#T26" title="EXTREAL2:th.26">EXTREAL2:26</a></i>;<br/><span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g1</font> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> = 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">g1</font> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p4">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
<b>by </b><i><a class="ref" href="supinf_2.html#T18" title="SUPINF_2:th.18">SUPINF_2:18</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">g1</font> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p0">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p5">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
<b>by </b><i><a class="ref" href="extreal1.html#T9" title="EXTREAL1:th.9">EXTREAL1:9</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</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" title="SUPINF_2:func.3">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p1">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c2">g1</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p5">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
<b>by </b><i><a class="txt" href="mesfunc5.html#E3:77_1_2_1_1"><i><font color="Green" title="E77">A7</font></i></a>, <a class="txt" href="mesfunc5.html#E28:77_1_2_1_1"><i><font color="Green" title="E89">A19</font></i></a>, <a class="ref" href="extreal1.html#T8" title="EXTREAL1:th.8">EXTREAL1:8</a></i>
<br/>.= 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</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" title="SUPINF_2:func.3">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p0">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c2">g1</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p5">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
<b>by </b><i><a class="txt" href="mesfunc5.html#E5:77_1_2_1_1"><i><font color="Green" title="E78">A8</font></i></a>, <a class="txt" href="mesfunc5.html#E27:77_1_2_1_1"><i><font color="Green" title="E88">A18</font></i></a>, <a class="ref" href="extreal1.html#T11" title="EXTREAL1:th.11">EXTREAL1:11</a></i>
;<br/><a NAME="E30:77_1_2_1_1"/><b>then </b>
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g1</font> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p5">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <font color="Maroon" title="c2">g1</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E27:77_1_2_1_1"><i><font color="Green" title="E88">A18</font></i></a>, <a class="ref" href="extreal2.html#T61" title="EXTREAL2:th.61">EXTREAL2:61</a></i>;<br/><a NAME="E31:77_1_2_1_1"/><b>then </b><i><font color="Green" title="E90">A20</font></i>: 
<span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">g1</font> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c2">g1</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1"><a href="extreal1.html#K4" title="EXTREAL1:func.4">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">seq</font> <a href="measure1.html#K1" title="MEASURE1:func.1">.</a> <span class="p4">(<span class="default"><a href="limfunc1.html#K1" title="LIMFUNC1:func.1">max</a> <font color="Maroon" title="c8">n1</font>,<font color="Maroon" title="c9">n2</font></span>)</span></span>)</span> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font></span>)</span></span><a href="extreal1.html#K4" title="EXTREAL1:func.4">.|</a></span>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E17:77_1_2_1_1"><i><font color="Green" title="E83">A13</font></i></a>, <a class="ref" href="extreal2.html#T66" title="EXTREAL2:th.66">EXTREAL2:66</a></i>;<br/><a NAME="E32:77_1_2_1_1"/><i><font color="Green" title="E91">A21</font></i>: 
<span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <span class="p2">(<span class="default"><span class="p3"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="complex1.html#K16" title="COMPLEX1:func.16">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font></span>)</span></span><a href="complex1.html#K16" title="COMPLEX1:func.16">.|</a></span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="mesfunc5.html#T7" target="_self" title="MESFUNC5:th.7">Th7</a></i>;<br/><a NAME="E33:77_1_2_1_1"/>
<font color="Maroon" title="c11">g</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c12">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g1</font> <a href="supinf_2.html#K4" title="SUPINF_2:func.4">-</a> <font color="Maroon" title="c3">g2</font>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E3:77_1_2_1_1"><i><font color="Green" title="E77">A7</font></i></a>, <a class="txt" href="mesfunc5.html#E5:77_1_2_1_1"><i><font color="Green" title="E78">A8</font></i></a>, <a class="ref" href="supinf_2.html#T5" title="SUPINF_2:th.5">SUPINF_2:5</a></i>;<br/><b>hence </b><a NAME="E34:77_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="mesfunc5.html#E26:77_1_2_1_1"><i><font color="Green" title="E87">A17</font></i></a>, <a class="txt" href="mesfunc5.html#E31:77_1_2_1_1"><i><font color="Green" title="E90">A20</font></i></a>, <a class="txt" href="mesfunc5.html#E32:77_1_2_1_1"><i><font color="Green" title="E91">A21</font></i></a>, <a class="ref" href="extreal2.html#T49" title="EXTREAL2:th.49">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" title="c1">seq</font> is <a href="mesfunc5.html#V8" title="MESFUNC5:attr.8">convergent_to_+infty</a> or <font color="Maroon" title="c1">seq</font> is <a href="mesfunc5.html#V9" title="MESFUNC5:attr.9">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#E2:77_1_2"><i><font color="Green" title="E73">A3</font></i></a>, <a class="txt" href="mesfunc5.html#E3:77_1_2"><i><font color="Green" title="E74">A4</font></i></a>, <a class="txt" href="mesfunc5.html#E4:77_1_2"><i><font color="Green" title="E75">A5</font></i></a>, <a class="ref" href="mesfunc5.html#T56" target="_self" title="MESFUNC5:th.56">Th56</a>, <a class="ref" href="mesfunc5.html#T57" target="_self" title="MESFUNC5:th.57">Th57</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
