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

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:9_1_1"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>ex <font color="Olive">b<sub>2</sub></font> being <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( not <font color="Olive">b<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Olive">b<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>3</sub></font> being <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> holds <br/> <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <span class="p2">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <font color="Olive">b<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>and </b><br/><a NAME="E2:9_1_1"/><i><font color="Green">E10</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>ex <font color="Olive">b<sub>2</sub></font> being <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( not <font color="Olive">b<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Olive">b<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>3</sub></font> being <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> holds <br/> <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binop_2.html#K10">-</a> <span class="p2">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <font color="Olive">b<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> ) )
 ;<br/>

<div><i><font color="Green">E11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>assume </b><a NAME="E1:9_1_1_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K7">/</a> 2;<br/><a NAME="E2:9_1_1_1"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K7">/</a> 2 is   <a href="real_1.html#NM1">Real</a> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="bhsp_6.html#E1:9_1_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="real_2.html#T127">REAL_2:127</a>, <a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/><a NAME="E3:9_1_1_1"/><i><font color="Green">E14</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:9_1_1_1"/><i><font color="Green">E15</font></i>: 
( not <font color="Maroon">c<sub>8</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> holds <br/> <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <span class="p2">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <font color="Olive">b<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K7">/</a> 2 ) )
 <b>by </b><i><a class="txt" href="bhsp_6.html#E1:9_1_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="bhsp_6.html#E2:9_1_1_1"><i><font color="Green">E13</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>9</sub></font> being  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:9_1_1_1"/><i><font color="Green">E16</font></i>: 
( not <font color="Maroon">c<sub>9</sub></font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> holds <br/> <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binop_2.html#K10">-</a> <span class="p2">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <font color="Olive">b<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K7">/</a> 2 ) )
 <b>by </b><i><a class="txt" href="bhsp_6.html#E2:9_1_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="bhsp_6.html#E2:9_1_1_1"><i><font color="Green">E13</font></i></a></i>;<br/><b>set </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font>;<br/><a NAME="E8:9_1_1_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E5:9_1_1_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="bhsp_6.html#E7:9_1_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/><a NAME="E9:9_1_1_1"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font> is  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E10:9_1_1_1"/><b>then </b><i><font color="Green">E18</font></i>: 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <span class="p2">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="bhsp_6.html#E5:9_1_1_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="bhsp_6.html#E8:9_1_1_1"><i><font color="Green">E17</font></i></a></i>;<br/><a NAME="E11:9_1_1_1"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font> is  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E12:9_1_1_1"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binop_2.html#K10">-</a> <span class="p2">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="bhsp_6.html#E7:9_1_1_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="bhsp_6.html#E8:9_1_1_1"><i><font color="Green">E17</font></i></a></i>;<br/><a NAME="E13:9_1_1_1"/><i><font color="Green">E20</font></i>: 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span> <a href="binop_2.html#K10">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="complex1.html#T143">COMPLEX1:143</a></i>;<br/><a NAME="E14:9_1_1_1"/>
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="binop_2.html#K10">-</a> <span class="p3">(<span class="default"><a href="bhsp_5.html#K5">setopfunc</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<a href="numbers.html#K1">REAL</a> ,<font color="Maroon">c<sub>3</sub></font>,<a href="binop_2.html#K33">addreal</a> </span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E3:9_1_1_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="bhsp_6.html#E10:9_1_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="bhsp_6.html#E12:9_1_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/><b>hence </b><a NAME="E15:9_1_1_1"/>
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E13:9_1_1_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:9_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:9_1_1_2"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:9_1_1_2"/><i><font color="Green">E13</font></i>: 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:9_1_1_2_1"/>
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:9_1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="absvalue.html#T7">ABSVALUE:7</a></i>;<br/>
<b>hence </b><a NAME="E3:9_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="bhsp_6.html#E1:9_1_1_2"><i><font color="Green">E12</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:9_1_1_2"/>
0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="complex1.html#T132">COMPLEX1:132</a></i>;<br/>
<b>hence </b><a NAME="E4:9_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="bhsp_6.html#E3:9_1_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="bhsp_6.html#E2:9_1_1_2"><i><font color="Green">E13</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:9_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>


</div>
