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

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="complsp1.html#K1" title="COMPLSP1:func.1">the_Complex_Space</a> <font color="Maroon" title="c1">n</font> is  <a href="pre_topc.html#V8" title="PRE_TOPC:attr.8">T_2</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K1" title="COMPLSP1:func.1">the_Complex_Space</a> <font color="Maroon" title="c1">n</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K1" title="COMPLSP1:func.1">the_Complex_Space</a> <font color="Maroon" title="c1">n</font></span>)</span>  holds <br/>( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or  ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">K10</a>( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K1" title="COMPLSP1:func.1">the_Complex_Space</a> <font color="Maroon" title="c1">n</font></span>)</span>) st <br/>( <font color="Olive">b<sub>2</sub></font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Olive">b<sub>3</sub></font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive">b<sub>3</sub></font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">q</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K1" title="COMPLSP1:func.1">the_Complex_Space</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font> or  ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">K10</a>( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K1" title="COMPLSP1:func.1">the_Complex_Space</a> <font color="Maroon" title="c1">n</font></span>)</span>) st <br/>( <font color="Olive">b<sub>1</sub></font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Olive">b<sub>2</sub></font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive">b<sub>2</sub></font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:5"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">K10</a>( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K1" title="COMPLSP1:func.1">the_Complex_Space</a> <font color="Maroon" title="c1">n</font></span>)</span>) st <br/>( <font color="Olive">b<sub>1</sub></font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Olive">b<sub>2</sub></font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive">b<sub>2</sub></font> )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">z1</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c5">z2</font> = <font color="Maroon" title="c3">q</font> as    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">d</font> = <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">K1</font> =  <a href="seq_4.html#K23" title="SEQ_4:func.23">Ball</a> (<font color="Maroon" title="c4">z1</font>,<span class="p1">(<span class="default"><span class="p2"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2</span>)</span>), <font color="Maroon" title="c8">K2</font> =  <a href="seq_4.html#K23" title="SEQ_4:func.23">Ball</a> (<font color="Maroon" title="c5">z2</font>,<span class="p1">(<span class="default"><span class="p2"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2</span>)</span>) as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K1" title="COMPLSP1:func.1">the_Complex_Space</a> <font color="Maroon" title="c1">n</font></span>)</span> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c7">K1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">K10</a>( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K1" title="COMPLSP1:func.1">the_Complex_Space</a> <font color="Maroon" title="c1">n</font></span>)</span>) st <br/>( <font color="Maroon" title="c7">K1</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">K1</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon" title="c7">K1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive">b<sub>1</sub></font> )</span><br/>

<span class="kw">take </span>
<font color="Maroon" title="c8">K2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c7">K1</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Maroon" title="c8">K2</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">K1</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K2</font> &amp; <font color="Maroon" title="c7">K1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c8">K2</font> )</span><br/>

<a NAME="E4:5"/>
(  <a href="seq_4.html#K23" title="SEQ_4:func.23">Ball</a> (<font color="Maroon" title="c4">z1</font>,<span class="p1">(<span class="default"><span class="p2"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2</span>)</span>) is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  &amp;  <a href="seq_4.html#K23" title="SEQ_4:func.23">Ball</a> (<font color="Maroon" title="c5">z2</font>,<span class="p1">(<span class="default"><span class="p2"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2</span>)</span>) is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#T112" title="SEQ_4:th.112">SEQ_4:112</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:5"/>
( <font color="Maroon" title="c7">K1</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Maroon" title="c8">K2</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="complsp1.html#T4" target="_self" title="COMPLSP1:th.4">Th6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">K1</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K2</font> &amp; <font color="Maroon" title="c7">K1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c8">K2</font> )</span><br/>

<a NAME="E6:5"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:5"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="seq_4.html#T103" title="SEQ_4:th.103">SEQ_4:103</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:5"/>
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">K1</font> &amp; <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#T111" title="SEQ_4:th.111">SEQ_4:111</a>, <a class="ref" href="xreal_1.html#T215" title="XREAL_1:th.215">XREAL_1:215</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">K1</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c8">K2</font></span><br/>

<span class="kw">assume </span><a NAME="E8:5"/>
<font color="Maroon" title="c7">K1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c8">K2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">x</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font><span class="kw"> such that </span><br/><a NAME="E10:5"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="seq_4.html#K23" title="SEQ_4:func.23">Ball</a> (<font color="Maroon" title="c4">z1</font>,<span class="p2">(<span class="default"><span class="p3"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2</span>)</span>)</span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="seq_4.html#K23" title="SEQ_4:func.23">Ball</a> (<font color="Maroon" title="c5">z2</font>,<span class="p2">(<span class="default"><span class="p3"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#T4" title="SUBSET_1:th.4">SUBSET_1:4</a></span>;<br/>
<a NAME="E11:5"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">K2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:5"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E12:5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A3</font></span>: 
<span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c9">x</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#T110" title="SEQ_4:th.110">SEQ_4:110</a></span>;<br/>
<a NAME="E13:5"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">K1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:5"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E14:5"/><span class="kw">then </span>
<span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c9">x</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#T110" title="SEQ_4:th.110">SEQ_4:110</a></span>;<br/>
<a NAME="E15:5"/><span class="kw">then </span>
<span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c9">x</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c9">x</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2</span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K12" title="BINOP_2:func.12">/</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:5"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/>
<a NAME="E16:5"/><span class="kw">then </span>
<span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c9">x</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">x</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="seq_4.html#K19" title="SEQ_4:func.19">-</a> <font color="Maroon" title="c5">z2</font></span>)</span></span><a href="seq_4.html#K22" title="SEQ_4:func.22">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#T104" title="SEQ_4:th.104">SEQ_4:104</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#T105" title="SEQ_4:th.105">SEQ_4:105</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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