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

<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">f1</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">X</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> ;<br/>



<b>assume </b><a NAME="E1:26"/><i><font color="Green" title="E31">A1</font></i>: 
( <font color="Maroon" title="c2">f1</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> &amp; ( for <font color="Olive" title="b1">q</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>  holds <font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 ) )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>for <font color="Olive" title="b1">r1</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Maroon" title="c2">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r1</font> holds <br/>$2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Olive" title="b1">r1</font>;<br/>
<a NAME="E2:26"/><i><font color="Green" title="E32">A2</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  ex <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c4">r1</font> = <font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/>
<b>set </b><font color="Maroon" title="c5">r3</font> = 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c4">r1</font>;<br/>
<a NAME="E2:26_1"/>
for <font color="Olive" title="b1">r1</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r1</font> holds <br/>1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c4">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Olive" title="b1">r1</font>
 
;<br/>
<b>hence </b><a NAME="E3:26_1"/>
 ex <font color="Olive" title="b1">y</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <br/>for <font color="Olive" title="b2">r1</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">r1</font> holds <br/><font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Olive" title="b2">r1</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:26"/>
 ex <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <br/>for <font color="Olive" title="b2">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font>]
 
<b>from </b><i><a class="ref" href="funct_2.html#S3" title="FUNCT_2:sch.3">FUNCT_2:sch 3</a>(<a class="txt" href="jgraph_2.html#E2:26"><i><font color="Green" title="E32">A2</font></i></a>);<br/></i>
<b>then consider </b><font color="Maroon" title="c3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <b> such that </b><br/><a NAME="E5:26"/><i><font color="Green" title="E33">A3</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">r1</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">r1</font> holds <br/><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Olive" title="b2">r1</font>
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c4">g0</font> = <font color="Maroon" title="c3">f</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">X</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/>
<a NAME="E7:26"/><i><font color="Green" title="E34">A4</font></i>: 
for <font color="Olive" title="b1">p</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">r1</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 <font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">r1</font> holds <br/><font color="Maroon" title="c4">g0</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b2">r1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c6">r1</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>



<b>assume </b><a NAME="E1:26_2"/><i><font color="Green" title="E35">A5</font></i>: 
<font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">r1</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c7">r1</font> = <font color="Maroon" title="c6">r1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.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="E3:26_2"/>
<font color="Maroon" title="c4">g0</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E5:26"><i><font color="Green" title="E33">A3</font></i></a>, <a class="txt" href="jgraph_2.html#E1:26_2"><i><font color="Green" title="E35">A5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:26_2"/>
<font color="Maroon" title="c4">g0</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Maroon" title="c6">r1</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E8:26"/>
for <font color="Olive" title="b1">p</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">V</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>   st <font color="Maroon" title="c4">g0</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">V</font> &amp; <font color="Olive" title="b2">V</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> holds <br/> ex <font color="Olive" title="b3">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">W</font> &amp; <font color="Olive" title="b3">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c4">g0</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b3">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">V</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c6">V</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a> ;<br/>



<b>assume </b><a NAME="E1:26_3"/><i><font color="Green" title="E35">A6</font></i>: 
( <font color="Maroon" title="c4">g0</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">V</font> &amp; <font color="Maroon" title="c6">V</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c7">r</font> = <font color="Maroon" title="c4">g0</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">p</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">r0</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E4:26_3"/><i><font color="Green" title="E36">A7</font></i>: 
( <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp; <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">V</font> )
 <b>by </b><i><a class="txt" href="jgraph_2.html#E1:26_3"><i><font color="Green" title="E35">A6</font></i></a>, <a class="ref" href="frechet.html#T8" title="FRECHET:th.8">FRECHET:8</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">r1</font> = <font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">p</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/>
<a NAME="E6:26_3"/><i><font color="Green" title="E37">A8</font></i>: 
<font color="Maroon" title="c9">r1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E1:26"><i><font color="Green" title="E31">A1</font></i></a></i>;<br/>
<a NAME="E7:26_3"/><i><font color="Green" title="E38">A9</font></i>: 
<font color="Maroon" title="c7">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">r1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E5:26"><i><font color="Green" title="E33">A3</font></i></a></i>;<br/>
<a NAME="E8:26_3"/><b>then </b><i><font color="Green" title="E39">A10</font></i>: 
<font color="Maroon" title="c7">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> 
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T217" title="XCMPLX_1:th.217">XCMPLX_1:217</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_3_1_1"/>
( <font color="Maroon" title="c9">r1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 or <font color="Maroon" title="c9">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_3_1_1_1"><b>case </b></a><a NAME="E1:26_3_1_1_1"/><i><font color="Green" title="E40">A11</font></i>: 
<font color="Maroon" title="c9">r1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:26_3_1_1_1"/><b>then </b><i><font color="Green" title="E41">A12</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E6:26_3"><i><font color="Green" title="E37">A8</font></i></a>, <a class="txt" href="jgraph_2.html#E8:26_3"><i><font color="Green" title="E39">A10</font></i></a>, <a class="ref" href="xreal_1.html#T124" title="XREAL_1:th.124">XREAL_1:124</a></i>;<br/><a NAME="E3:26_3_1_1_1"/><i><font color="Green" title="E42">A13</font></i>: 
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/><a NAME="E4:26_3_1_1_1"/><b>then </b><i><font color="Green" title="E43">A14</font></i>: 
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E6:26_3"><i><font color="Green" title="E37">A8</font></i></a>, <a class="txt" href="jgraph_2.html#E8:26_3"><i><font color="Green" title="E39">A10</font></i></a>, <a class="txt" href="jgraph_2.html#E1:26_3_1_1_1"><i><font color="Green" title="E40">A11</font></i></a>, <a class="ref" href="xreal_1.html#T124" title="XREAL_1:th.124">XREAL_1:124</a></i>;<br/><a NAME="E5:26_3_1_1_1"/><i><font color="Green" title="E44">A15</font></i>: 
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E6:26_3_1_1_1"/><b>then </b><i><font color="Green" title="E45">A16</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E2:26_3_1_1_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="txt" href="jgraph_2.html#E3:26_3_1_1_1"><i><font color="Green" title="E42">A13</font></i></a></i>;<br/><a NAME="E7:26_3_1_1_1"/>
<font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1
 <b>by </b><i><a class="txt" href="jgraph_2.html#E2:26_3_1_1_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><a NAME="E8:26_3_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r1</font>
 ;<br/><a NAME="E9:26_3_1_1_1"/><b>then </b><i><font color="Green" title="E46">A17</font></i>: 
1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r1</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E6:26_3"><i><font color="Green" title="E37">A8</font></i></a>, <a class="txt" href="jgraph_2.html#E7:26_3"><i><font color="Green" title="E38">A9</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><b>set </b><font color="Maroon" title="c10">r4</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span>;<br/><a NAME="E10:26_3_1_1_1"/><i><font color="Green" title="E47">A18</font></i>: 
<font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="txt" href="jgraph_2.html#E2:26_3_1_1_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="ref" href="real_2.html#T127" title="REAL_2:th.127">REAL_2:127</a></i>;<br/><a NAME="E11:26_3_1_1_1"/><i><font color="Green" title="E48">A19</font></i>: 
<font color="Maroon" title="c7">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E12:26_3_1_1_1"/><b>then </b><i><font color="Green" title="E49">A20</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E2:26_3_1_1_1"><i><font color="Green" title="E41">A12</font></i></a></i>;<br/><a NAME="E13:26_3_1_1_1"/><b>then </b><i><font color="Green" title="E50">A21</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E10:26_3_1_1_1"><i><font color="Green" title="E47">A18</font></i></a>, <a class="ref" href="real_2.html#T127" title="REAL_2:th.127">REAL_2:127</a></i>;<br/><i><font color="Green" title="E51">A22</font></i>: <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_2.html#E9:26_3_1_1_1"><i><font color="Green" title="E46">A17</font></i></a>, <a class="ref" href="xcmplx_1.html#T48" title="XCMPLX_1:th.48">XCMPLX_1:48</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121" title="XCMPLX_1:th.121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font>
<b>by </b><i><a class="txt" href="jgraph_2.html#E2:26_3_1_1_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="txt" href="jgraph_2.html#E11:26_3_1_1_1"><i><font color="Green" title="E48">A19</font></i></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121" title="XCMPLX_1:th.121">XCMPLX_1:121</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font>

;<br/><a NAME="E15:26_3_1_1_1"/>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E2:26_3_1_1_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="txt" href="jgraph_2.html#E12:26_3_1_1_1"><i><font color="Green" title="E49">A20</font></i></a>, <a class="ref" href="real_2.html#T127" title="REAL_2:th.127">REAL_2:127</a></i>;<br/><a NAME="E16:26_3_1_1_1"/><b>then </b><i><font color="Green" title="E52">A23</font></i>: 
<font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E2:26_3_1_1_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="txt" href="jgraph_2.html#E14:26_3_1_1_1"><i><font color="Green" title="E51">A22</font></i></a>, <a class="ref" href="real_2.html#T127" title="REAL_2:th.127">REAL_2:127</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">G1</font> = <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/><a NAME="E18:26_3_1_1_1"/><i><font color="Green" title="E53">A24</font></i>: 
<font color="Maroon" title="c9">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E13:26_3_1_1_1"><i><font color="Green" title="E50">A21</font></i></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E19:26_3_1_1_1"/><b>then </b>
<font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">r1</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><a NAME="E20:26_3_1_1_1"/><b>then </b><i><font color="Green" title="E54">A25</font></i>: 
<font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">G1</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E18:26_3_1_1_1"><i><font color="Green" title="E53">A24</font></i></a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/><a NAME="E21:26_3_1_1_1"/>
<font color="Maroon" title="c11">G1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="ref" href="jordan6.html#T46" title="JORDAN6:th.46">JORDAN6:46</a></i>;<br/><b>then consider </b><font color="Maroon" title="c12">W1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E23:26_3_1_1_1"/><i><font color="Green" title="E55">A26</font></i>: 
( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">W1</font> &amp; <font color="Maroon" title="c12">W1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c2">f1</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c12">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">G1</font> )
 <b>by </b><i><a class="txt" href="jgraph_2.html#E1:26"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="jgraph_2.html#E20:26_3_1_1_1"><i><font color="Green" title="E54">A25</font></i></a>, <a class="ref" href="jgraph_2.html#T20" target="_self" title="JGRAPH_2:th.20">Th20</a></i>;<br/><b>set </b><font color="Maroon" title="c13">W</font> = <font color="Maroon" title="c12">W1</font>;<br/><a NAME="E24:26_3_1_1_1"/>
<font color="Maroon" title="c4">g0</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c12">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_3_1_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:26_3_1_1_1_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">g0</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c12">W1</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c15">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:26_3_1_1_1_2"/><i><font color="Green" title="E56">A27</font></i>: 
( <font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g0</font> &amp; <font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">W1</font> &amp; <font color="Maroon" title="c4">g0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">pz</font> = <font color="Maroon" title="c15">z</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_1_2"><i><font color="Green" title="E56">A27</font></i></a></i>;<br/>
<a NAME="E5:26_3_1_1_1_2"/>
<font color="Maroon" title="c16">pz</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
;<br/>
<a NAME="E6:26_3_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c16">pz</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E7:26_3_1_1_1_2"/><b>then </b><i><font color="Green" title="E57">A28</font></i>: 
<font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">pz</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">f1</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c12">W1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_1_2"><i><font color="Green" title="E56">A27</font></i></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">aa1</font> = <font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">pz</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/>
<a NAME="E9:26_3_1_1_1_2"/><i><font color="Green" title="E58">A29</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c17">aa1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E5:26"><i><font color="Green" title="E33">A3</font></i></a>, <a class="txt" href="jgraph_2.html#E3:26_3_1_1_1_2"><i><font color="Green" title="E56">A27</font></i></a></i>;<br/>
<a NAME="E10:26_3_1_1_1_2"/><i><font color="Green" title="E59">A30</font></i>: 
( <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c17">aa1</font> &amp; <font color="Maroon" title="c17">aa1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E23:26_3_1_1_1"><i><font color="Green" title="E55">A26</font></i></a>, <a class="txt" href="jgraph_2.html#E7:26_3_1_1_1_2"><i><font color="Green" title="E57">A28</font></i></a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/>
<a NAME="E11:26_3_1_1_1_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c17">aa1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E16:26_3_1_1_1"><i><font color="Green" title="E52">A23</font></i></a></i>;<br/>
<a NAME="E12:26_3_1_1_1_2"/><b>then </b><i><font color="Green" title="E60">A31</font></i>: 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c17">aa1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E9:26_3_1_1_1"><i><font color="Green" title="E46">A17</font></i></a>, <a class="txt" href="jgraph_2.html#E10:26_3_1_1_1_2"><i><font color="Green" title="E59">A30</font></i></a>, <a class="ref" href="real_2.html#T200" title="REAL_2:th.200">REAL_2:200</a></i>;<br/>
<a NAME="E13:26_3_1_1_1_2"/><i><font color="Green" title="E61">A32</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="square_1.html#T74" title="SQUARE_1:th.74">SQUARE_1:74</a></i>;<br/>
<a NAME="E14:26_3_1_1_1_2"/><b>then </b>
0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </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="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<a NAME="E15:26_3_1_1_1_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E13:26_3_1_1_1_2"><i><font color="Green" title="E61">A32</font></i></a></i>;<br/>
<a NAME="E16:26_3_1_1_1_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 
;<br/>
<a NAME="E17:26_3_1_1_1_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span>
 
;<br/>
<a NAME="E18:26_3_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/>
<a NAME="E19:26_3_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">r</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/>
<a NAME="E20:26_3_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">r</font></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="c7">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c7">r</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<a NAME="E21:26_3_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></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="c7">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E6:26_3_1_1_1"><i><font color="Green" title="E45">A16</font></i></a>, <a class="ref" href="real_1.html#T73" title="REAL_1:th.73">REAL_1:73</a></i>;<br/>
<a NAME="E22:26_3_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3_1_1_1"><i><font color="Green" title="E43">A14</font></i></a>, <a class="txt" href="jgraph_2.html#E5:26_3_1_1_1"><i><font color="Green" title="E44">A15</font></i></a>, <a class="ref" href="xcmplx_1.html#T90" title="XCMPLX_1:th.90">XCMPLX_1:90</a></i>;<br/>
<a NAME="E23:26_3_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">r</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T78" title="XCMPLX_1:th.78">XCMPLX_1:78</a></i>;<br/>
<a NAME="E24:26_3_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">r</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63" title="XCMPLX_1:th.63">XCMPLX_1:63</a></i>;<br/>
<a NAME="E25:26_3_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E2:26_3_1_1_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="txt" href="jgraph_2.html#E11:26_3_1_1_1"><i><font color="Green" title="E48">A19</font></i></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></i>;<br/>
<a NAME="E26:26_3_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T78" title="XCMPLX_1:th.78">XCMPLX_1:78</a></i>;<br/>
<a NAME="E27:26_3_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63" title="XCMPLX_1:th.63">XCMPLX_1:63</a></i>;<br/>
<a NAME="E28:26_3_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T48" title="XCMPLX_1:th.48">XCMPLX_1:48</a></i>;<br/>
<a NAME="E29:26_3_1_1_1_2"/><b>then </b><i><font color="Green" title="E62">A33</font></i>: 
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c17">aa1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E12:26_3_1_1_1_2"><i><font color="Green" title="E60">A31</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E30:26_3_1_1_1_2"/><i><font color="Green" title="E63">A34</font></i>: 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c17">aa1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E16:26_3_1_1_1"><i><font color="Green" title="E52">A23</font></i></a>, <a class="txt" href="jgraph_2.html#E10:26_3_1_1_1_2"><i><font color="Green" title="E59">A30</font></i></a>, <a class="ref" href="real_2.html#T151" title="REAL_2:th.151">REAL_2:151</a></i>;<br/>
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> = 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9" title="XCMPLX_0:def.9">XCMPLX_0:def 9</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T217" title="XCMPLX_1:th.217">XCMPLX_1:217</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">r1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_2.html#E9:26_3_1_1_1"><i><font color="Green" title="E46">A17</font></i></a>, <a class="ref" href="xcmplx_1.html#T78" title="XCMPLX_1:th.78">XCMPLX_1:78</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T82" title="XCMPLX_1:th.82">XCMPLX_1:82</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">r1</font></span>)</span>

<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">r1</font></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_2.html#E2:26_3_1_1_1"><i><font color="Green" title="E41">A12</font></i></a>, <a class="txt" href="jgraph_2.html#E3:26_3_1_1_1"><i><font color="Green" title="E42">A13</font></i></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">r1</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121" title="XCMPLX_1:th.121">XCMPLX_1:121</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">r1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T82" title="XCMPLX_1:th.82">XCMPLX_1:82</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">r1</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T78" title="XCMPLX_1:th.78">XCMPLX_1:78</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">r1</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1
<b>by </b><i><a class="ref" href="xcmplx_1.html#T81" title="XCMPLX_1:th.81">XCMPLX_1:81</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 1
<b>by </b><i><a class="txt" href="jgraph_2.html#E6:26_3"><i><font color="Green" title="E37">A8</font></i></a>, <a class="txt" href="jgraph_2.html#E8:26_3"><i><font color="Green" title="E39">A10</font></i></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></i>
<br/>.= 
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font>

;<br/>
<b>hence </b><a NAME="E32:26_3_1_1_1_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E9:26_3_1_1_1_2"><i><font color="Green" title="E58">A29</font></i></a>, <a class="txt" href="jgraph_2.html#E29:26_3_1_1_1_2"><i><font color="Green" title="E62">A33</font></i></a>, <a class="txt" href="jgraph_2.html#E30:26_3_1_1_1_2"><i><font color="Green" title="E63">A34</font></i></a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/>


</div><b>end;</b></div><a NAME="E25:26_3_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">g0</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c12">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">V</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>hence </b><a NAME="E26:26_3_1_1_1"/>
 ex <font color="Olive" title="b1">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp; <font color="Olive" title="b1">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c4">g0</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">V</font> )
 <b>by </b><i><a class="txt" href="jgraph_2.html#E23:26_3_1_1_1"><i><font color="Green" title="E55">A26</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_3_1_1_2"><b>case </b></a><a NAME="E1:26_3_1_1_2"/>
<font color="Maroon" title="c9">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:26_3_1_1_2"/><b>then </b><i><font color="Green" title="E40">A35</font></i>: 
<font color="Maroon" title="c9">r1</font> <a href="real_1.html#K2" title="REAL_1:func.2">"</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 <b>by </b><i><a class="ref" href="real_2.html#T149" title="REAL_2:th.149">REAL_2:149</a></i>;<br/><a NAME="E3:26_3_1_1_2"/><b>then </b><i><font color="Green" title="E41">A36</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E8:26_3"><i><font color="Green" title="E39">A10</font></i></a>, <a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/><a NAME="E4:26_3_1_1_2"/><i><font color="Green" title="E42">A37</font></i>: 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/><a NAME="E5:26_3_1_1_2"/><b>then </b><i><font color="Green" title="E43">A38</font></i>: 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E8:26_3"><i><font color="Green" title="E39">A10</font></i></a>, <a class="txt" href="jgraph_2.html#E2:26_3_1_1_2"><i><font color="Green" title="E40">A35</font></i></a>, <a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/><a NAME="E6:26_3_1_1_2"/><i><font color="Green" title="E44">A39</font></i>: 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E7:26_3_1_1_2"/><b>then </b><i><font color="Green" title="E45">A40</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2"><i><font color="Green" title="E41">A36</font></i></a>, <a class="txt" href="jgraph_2.html#E4:26_3_1_1_2"><i><font color="Green" title="E42">A37</font></i></a></i>;<br/><a NAME="E8:26_3_1_1_2"/>
<font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1
 <b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2"><i><font color="Green" title="E41">A36</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><a NAME="E9:26_3_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r1</font>
 ;<br/><a NAME="E10:26_3_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">r1</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r1</font>
 ;<br/><a NAME="E11:26_3_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r1</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E6:26_3"><i><font color="Green" title="E37">A8</font></i></a>, <a class="txt" href="jgraph_2.html#E7:26_3"><i><font color="Green" title="E38">A9</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><a NAME="E12:26_3_1_1_2"/><b>then </b><i><font color="Green" title="E46">A41</font></i>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r1</font>
 ;<br/><a NAME="E13:26_3_1_1_2"/><b>then </b><i><font color="Green" title="E47">A42</font></i>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c9">r1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span>
 ;<br/><b>set </b><font color="Maroon" title="c10">r4</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span>;<br/><a NAME="E14:26_3_1_1_2"/><i><font color="Green" title="E48">A43</font></i>: 
<font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="txt" href="jgraph_2.html#E3:26_3_1_1_2"><i><font color="Green" title="E41">A36</font></i></a>, <a class="ref" href="real_2.html#T127" title="REAL_2:th.127">REAL_2:127</a></i>;<br/><a NAME="E15:26_3_1_1_2"/><i><font color="Green" title="E49">A44</font></i>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E16:26_3_1_1_2"/><b>then </b><i><font color="Green" title="E50">A45</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2"><i><font color="Green" title="E41">A36</font></i></a></i>;<br/><a NAME="E17:26_3_1_1_2"/><b>then </b><i><font color="Green" title="E51">A46</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E14:26_3_1_1_2"><i><font color="Green" title="E48">A43</font></i></a>, <a class="ref" href="real_2.html#T127" title="REAL_2:th.127">REAL_2:127</a></i>;<br/><i><font color="Green" title="E52">A47</font></i>: <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_2.html#E12:26_3_1_1_2"><i><font color="Green" title="E46">A41</font></i></a>, <a class="ref" href="xcmplx_1.html#T48" title="XCMPLX_1:th.48">XCMPLX_1:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188" title="XCMPLX_1:th.188">XCMPLX_1:188</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63" title="XCMPLX_1:th.63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2"><i><font color="Green" title="E41">A36</font></i></a>, <a class="txt" href="jgraph_2.html#E15:26_3_1_1_2"><i><font color="Green" title="E49">A44</font></i></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188" title="XCMPLX_1:th.188">XCMPLX_1:188</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63" title="XCMPLX_1:th.63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span>

;<br/><a NAME="E19:26_3_1_1_2"/>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2"><i><font color="Green" title="E41">A36</font></i></a>, <a class="txt" href="jgraph_2.html#E16:26_3_1_1_2"><i><font color="Green" title="E50">A45</font></i></a>, <a class="ref" href="real_2.html#T127" title="REAL_2:th.127">REAL_2:127</a></i>;<br/><a NAME="E20:26_3_1_1_2"/><b>then </b>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T188" title="XCMPLX_1:th.188">XCMPLX_1:188</a></i>;<br/><a NAME="E21:26_3_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60" title="XREAL_1:th.60">XREAL_1:60</a></i>;<br/><a NAME="E22:26_3_1_1_2"/><b>then </b><i><font color="Green" title="E53">A48</font></i>: 
<font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 0
 <b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2"><i><font color="Green" title="E41">A36</font></i></a>, <a class="txt" href="jgraph_2.html#E18:26_3_1_1_2"><i><font color="Green" title="E52">A47</font></i></a>, <a class="ref" href="real_2.html#T128" title="REAL_2:th.128">REAL_2:128</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">G1</font> = <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/><a NAME="E24:26_3_1_1_2"/><i><font color="Green" title="E54">A49</font></i>: 
<font color="Maroon" title="c9">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E17:26_3_1_1_2"><i><font color="Green" title="E51">A46</font></i></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><a NAME="E25:26_3_1_1_2"/><b>then </b>
<font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">r1</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><a NAME="E26:26_3_1_1_2"/><b>then </b><i><font color="Green" title="E55">A50</font></i>: 
<font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">G1</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E24:26_3_1_1_2"><i><font color="Green" title="E54">A49</font></i></a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/><a NAME="E27:26_3_1_1_2"/>
<font color="Maroon" title="c11">G1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="ref" href="jordan6.html#T46" title="JORDAN6:th.46">JORDAN6:46</a></i>;<br/><b>then consider </b><font color="Maroon" title="c12">W1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E29:26_3_1_1_2"/><i><font color="Green" title="E56">A51</font></i>: 
( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">W1</font> &amp; <font color="Maroon" title="c12">W1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c2">f1</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c12">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">G1</font> )
 <b>by </b><i><a class="txt" href="jgraph_2.html#E1:26"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="jgraph_2.html#E26:26_3_1_1_2"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="jgraph_2.html#T20" target="_self" title="JGRAPH_2:th.20">Th20</a></i>;<br/><b>set </b><font color="Maroon" title="c13">W</font> = <font color="Maroon" title="c12">W1</font>;<br/><a NAME="E30:26_3_1_1_2"/>
<font color="Maroon" title="c4">g0</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c12">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_3_1_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:26_3_1_1_2_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">g0</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c12">W1</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c15">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:26_3_1_1_2_2"/><i><font color="Green" title="E57">A52</font></i>: 
( <font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">g0</font> &amp; <font color="Maroon" title="c15">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">W1</font> &amp; <font color="Maroon" title="c4">g0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">pz</font> = <font color="Maroon" title="c15">z</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2_2"><i><font color="Green" title="E57">A52</font></i></a></i>;<br/>
<a NAME="E5:26_3_1_1_2_2"/>
<font color="Maroon" title="c16">pz</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
;<br/>
<a NAME="E6:26_3_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c16">pz</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">f1</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E7:26_3_1_1_2_2"/><b>then </b><i><font color="Green" title="E58">A53</font></i>: 
<font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">pz</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">f1</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c12">W1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2_2"><i><font color="Green" title="E57">A52</font></i></a>, <a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">aa1</font> = <font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">pz</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="topmetr.html#T24" title="TOPMETR:th.24">TOPMETR:24</a></i>;<br/>
<a NAME="E9:26_3_1_1_2_2"/><i><font color="Green" title="E59">A54</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c17">aa1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E5:26"><i><font color="Green" title="E33">A3</font></i></a>, <a class="txt" href="jgraph_2.html#E3:26_3_1_1_2_2"><i><font color="Green" title="E57">A52</font></i></a></i>;<br/>
<a NAME="E10:26_3_1_1_2_2"/><i><font color="Green" title="E60">A55</font></i>: 
( <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c17">aa1</font> &amp; <font color="Maroon" title="c17">aa1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E29:26_3_1_1_2"><i><font color="Green" title="E56">A51</font></i></a>, <a class="txt" href="jgraph_2.html#E7:26_3_1_1_2_2"><i><font color="Green" title="E58">A53</font></i></a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/>
<a NAME="E11:26_3_1_1_2_2"/><b>then </b>
0 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c17">aa1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E22:26_3_1_1_2"><i><font color="Green" title="E53">A48</font></i></a></i>;<br/>
<a NAME="E12:26_3_1_1_2_2"/><b>then </b><i><font color="Green" title="E61">A56</font></i>: 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c17">aa1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E12:26_3_1_1_2"><i><font color="Green" title="E46">A41</font></i></a>, <a class="txt" href="jgraph_2.html#E10:26_3_1_1_2_2"><i><font color="Green" title="E60">A55</font></i></a>, <a class="ref" href="real_2.html#T200" title="REAL_2:th.200">REAL_2:200</a></i>;<br/>
<a NAME="E13:26_3_1_1_2_2"/><i><font color="Green" title="E62">A57</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> 
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="square_1.html#T74" title="SQUARE_1:th.74">SQUARE_1:74</a></i>;<br/>
<a NAME="E14:26_3_1_1_2_2"/><b>then </b>
0 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </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="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<a NAME="E15:26_3_1_1_2_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E13:26_3_1_1_2_2"><i><font color="Green" title="E62">A57</font></i></a></i>;<br/>
<a NAME="E16:26_3_1_1_2_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 
;<br/>
<a NAME="E17:26_3_1_1_2_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span>
 
;<br/>
<a NAME="E18:26_3_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></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="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/>
<a NAME="E19:26_3_1_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/>
<a NAME="E20:26_3_1_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></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="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<a NAME="E21:26_3_1_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E7:26_3_1_1_2"><i><font color="Green" title="E45">A40</font></i></a>, <a class="ref" href="real_1.html#T73" title="REAL_1:th.73">REAL_1:73</a></i>;<br/>
<a NAME="E22:26_3_1_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E5:26_3_1_1_2"><i><font color="Green" title="E43">A38</font></i></a>, <a class="txt" href="jgraph_2.html#E6:26_3_1_1_2"><i><font color="Green" title="E44">A39</font></i></a>, <a class="ref" href="xcmplx_1.html#T90" title="XCMPLX_1:th.90">XCMPLX_1:90</a></i>;<br/>
<a NAME="E23:26_3_1_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T78" title="XCMPLX_1:th.78">XCMPLX_1:78</a></i>;<br/>
<a NAME="E24:26_3_1_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63" title="XCMPLX_1:th.63">XCMPLX_1:63</a></i>;<br/>
<a NAME="E25:26_3_1_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2"><i><font color="Green" title="E41">A36</font></i></a>, <a class="txt" href="jgraph_2.html#E15:26_3_1_1_2"><i><font color="Green" title="E49">A44</font></i></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></i>;<br/>
<a NAME="E26:26_3_1_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T78" title="XCMPLX_1:th.78">XCMPLX_1:78</a></i>;<br/>
<a NAME="E27:26_3_1_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T63" title="XCMPLX_1:th.63">XCMPLX_1:63</a></i>;<br/>
<a NAME="E28:26_3_1_1_2_2"/><b>then </b>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T48" title="XCMPLX_1:th.48">XCMPLX_1:48</a></i>;<br/>
<a NAME="E29:26_3_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="real_2.html#T109" title="REAL_2:th.109">REAL_2:109</a></i>;<br/>
<a NAME="E30:26_3_1_1_2_2"/><b>then </b>
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T189" title="XCMPLX_1:th.189">XCMPLX_1:189</a></i>;<br/>
<a NAME="E31:26_3_1_1_2_2"/><b>then </b><i><font color="Green" title="E63">A58</font></i>: 
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c17">aa1</font>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E12:26_3_1_1_2_2"><i><font color="Green" title="E61">A56</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E32:26_3_1_1_2_2"/><i><font color="Green" title="E64">A59</font></i>: 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c17">aa1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="jgraph_2.html#E22:26_3_1_1_2"><i><font color="Green" title="E53">A48</font></i></a>, <a class="txt" href="jgraph_2.html#E10:26_3_1_1_2_2"><i><font color="Green" title="E60">A55</font></i></a>, <a class="ref" href="real_2.html#T151" title="REAL_2:th.151">REAL_2:151</a></i>;<br/>
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> = 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9" title="XCMPLX_0:def.9">XCMPLX_0:def 9</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T217" title="XCMPLX_1:th.217">XCMPLX_1:217</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_2.html#E13:26_3_1_1_2"><i><font color="Green" title="E47">A42</font></i></a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188" title="XCMPLX_1:th.188">XCMPLX_1:188</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Maroon" title="c9">r1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T78" title="XCMPLX_1:th.78">XCMPLX_1:78</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T82" title="XCMPLX_1:th.82">XCMPLX_1:82</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">r1</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<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="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">r0</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">r1</font></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2"><i><font color="Green" title="E41">A36</font></i></a>, <a class="txt" href="jgraph_2.html#E4:26_3_1_1_2"><i><font color="Green" title="E42">A37</font></i></a>, <a class="ref" href="xcmplx_1.html#T60" title="XCMPLX_1:th.60">XCMPLX_1:60</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<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="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">r1</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121" title="XCMPLX_1:th.121">XCMPLX_1:121</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c9">r1</font></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T189" title="XCMPLX_1:th.189">XCMPLX_1:189</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<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="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c9">r1</font></span>)</span></span>)</span>

<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c9">r1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T82" title="XCMPLX_1:th.82">XCMPLX_1:82</a></i>
<br/>.= 
1 <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c9">r1</font></span>)</span></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T78" title="XCMPLX_1:th.78">XCMPLX_1:78</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c9">r1</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 1
<b>by </b><i><a class="ref" href="xcmplx_1.html#T81" title="XCMPLX_1:th.81">XCMPLX_1:81</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="jgraph_2.html#E12:26_3_1_1_2"><i><font color="Green" title="E46">A41</font></i></a>, <a class="ref" href="xcmplx_1.html#T217" title="XCMPLX_1:th.217">XCMPLX_1:217</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> 1
<b>by </b><i><a class="txt" href="jgraph_2.html#E3:26_3_1_1_2"><i><font color="Green" title="E41">A36</font></i></a>, <a class="ref" href="xcmplx_0.html#D7" title="XCMPLX_0:def.7">XCMPLX_0:def 7</a></i>
<br/>.= 
<font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font>

;<br/>
<b>hence </b><a NAME="E34:26_3_1_1_2_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <font color="Maroon" title="c8">r0</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">r</font> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <font color="Maroon" title="c8">r0</font></span>)</span></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E9:26_3_1_1_2_2"><i><font color="Green" title="E59">A54</font></i></a>, <a class="txt" href="jgraph_2.html#E31:26_3_1_1_2_2"><i><font color="Green" title="E63">A58</font></i></a>, <a class="txt" href="jgraph_2.html#E32:26_3_1_1_2_2"><i><font color="Green" title="E64">A59</font></i></a>, <a class="ref" href="rcomp_1.html#T47" title="RCOMP_1:th.47">RCOMP_1:47</a></i>;<br/>


</div><b>end;</b></div><a NAME="E31:26_3_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">g0</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Maroon" title="c12">W1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">V</font>
 <b>by </b><i><a class="txt" href="jgraph_2.html#E4:26_3"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><b>hence </b><a NAME="E32:26_3_1_1_2"/>
 ex <font color="Olive" title="b1">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp; <font color="Olive" title="b1">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c4">g0</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">V</font> )
 <b>by </b><i><a class="txt" href="jgraph_2.html#E29:26_3_1_1_2"><i><font color="Green" title="E56">A51</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E10:26_3"/>
 ex <font color="Olive" title="b1">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">W</font> &amp; <font color="Olive" title="b1">W</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c4">g0</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <font color="Olive" title="b1">W</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">V</font> )
 ;<br/>


</div><b>end;</b></div>
<a NAME="E9:26"/><b>then </b>
<font color="Maroon" title="c4">g0</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>
 
<b>by </b><i><a class="ref" href="jgraph_2.html#T20" target="_self" title="JGRAPH_2:th.20">Th20</a></i>;<br/>
<b>hence </b><a NAME="E10:26"/>
 ex <font color="Olive" title="b1">g</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">X</font>,<a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  st <br/>( ( for <font color="Olive" title="b2">p</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b3">r1</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 <font color="Maroon" title="c2">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">r1</font> holds <br/><font color="Olive" title="b1">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b3">r1</font> ) &amp; <font color="Olive" title="b1">g</font> is <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> )
 <b>by </b><i><a class="txt" href="jgraph_2.html#E7:26"><i><font color="Green" title="E34">A4</font></i></a></i>;<br/>


</div>
