<?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#M2" title="SUBSET_1:mode.2">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">  for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b1">A</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  &amp; <font color="Olive" title="b2">B</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  holds <br/> for <font color="Olive" title="b3">C</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">B</font> holds <br/><font color="Olive" title="b3">C</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</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">A</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  &amp; <font color="Maroon" title="c3">B</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  implies  for <font color="Olive" title="b1">C</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">B</font> holds <br/><font color="Olive" title="b1">C</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:125"/><span class="lab"><font color="Green" title="E68">A1</font></span>: 
<font color="Maroon" title="c2">A</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a> 
 <span class="kw">and </span><br/><a NAME="E2:125"/><span class="lab"><font color="Green" title="E69">A2</font></span>: 
<font color="Maroon" title="c3">B</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</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" title="b1">C</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</a> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">B</font> holds <br/><font color="Olive" title="b1">C</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">C</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="seq_4.html#K14" title="SEQ_4:func.14">COMPLEX</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="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">B</font> implies <font color="Maroon" title="c4">C</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E3:125"/><span class="lab"><font color="Green" title="E70">A3</font></span>: 
<font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">B</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="c4">C</font> is  <a href="seq_4.html#V1" title="SEQ_4:attr.1">open</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <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="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="seq_4.html#D14" target="_self" title="SEQ_4:def.14">SEQ_4:def 14</a> <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="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> implies  ex <font color="Olive" title="b1">r</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">r</font> &amp; (  for <font color="Olive" title="b2">z</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>  st <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><font color="Olive" title="b2">z</font></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> <font color="Olive" title="b1">r</font> holds <br/><font color="Maroon" title="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Olive" title="b2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> ) ) )</span><br/>

<span class="kw">assume </span><a NAME="E4:125"/><span class="lab"><font color="Green" title="E71">A4</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</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" title="b1">r</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">r</font> &amp; (  for <font color="Olive" title="b2">z</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>  st <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><font color="Olive" title="b2">z</font></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> <font color="Olive" title="b1">r</font> holds <br/><font color="Maroon" title="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Olive" title="b2">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> ) )</span><br/>

<a NAME="E5:125"/><span class="kw">then </span>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:125"><span class="lab"><font color="Green" title="E70">A3</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">r1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E7:125"/><span class="lab"><font color="Green" title="E72">A5</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">r1</font>
 <span class="kw">and </span><br/><a NAME="E8:125"/><span class="lab"><font color="Green" title="E73">A6</font></span>: 
 for <font color="Olive" title="b1">z</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>  st <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><font color="Olive" title="b1">z</font></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> <font color="Maroon" title="c6">r1</font> holds <br/><font color="Maroon" title="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:125"><span class="lab"><font color="Green" title="E68">A1</font></span></a>, <a class="ref" href="seq_4.html#D14" target="_self" title="SEQ_4:def.14">Def17</a></span>;<br/>
<a NAME="E9:125"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:125"><span class="lab"><font color="Green" title="E70">A3</font></span></a>, <a class="txt" href="#E4:125"><span class="lab"><font color="Green" title="E71">A4</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">r2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E11:125"/><span class="lab"><font color="Green" title="E74">A7</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c7">r2</font>
 <span class="kw">and </span><br/><a NAME="E12:125"/><span class="lab"><font color="Green" title="E75">A8</font></span>: 
 for <font color="Olive" title="b1">z</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>  st <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><font color="Olive" title="b1">z</font></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> <font color="Maroon" title="c7">r2</font> holds <br/><font color="Maroon" title="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:125"><span class="lab"><font color="Green" title="E69">A2</font></span></a>, <a class="ref" href="seq_4.html#D14" target="_self" title="SEQ_4:def.14">Def17</a></span>;<br/>
<span class="kw">take </span>
 <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<font color="Maroon" title="c6">r1</font>,<font color="Maroon" title="c7">r2</font>)
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<font color="Maroon" title="c6">r1</font>,<font color="Maroon" title="c7">r2</font>) &amp; (  for <font color="Olive" title="b1">z</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>  st <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><font color="Olive" title="b1">z</font></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>  <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<font color="Maroon" title="c6">r1</font>,<font color="Maroon" title="c7">r2</font>) holds <br/><font color="Maroon" title="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E13:125"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<font color="Maroon" title="c6">r1</font>,<font color="Maroon" title="c7">r2</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:125"><span class="lab"><font color="Green" title="E72">A5</font></span></a>, <a class="txt" href="#E11:125"><span class="lab"><font color="Green" title="E74">A7</font></span></a>, <a class="ref" href="xxreal_0.html#T15" title="XXREAL_0:th.15">XXREAL_0:15</a></span>; <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" title="b1">z</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>  st <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><font color="Olive" title="b1">z</font></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>  <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<font color="Maroon" title="c6">r1</font>,<font color="Maroon" title="c7">r2</font>) holds <br/><font color="Maroon" title="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">z</font> be    <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><font color="Maroon" title="c8">z</font></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>  <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<font color="Maroon" title="c6">r1</font>,<font color="Maroon" title="c7">r2</font>) implies <font color="Maroon" title="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> )</span><br/>

<span class="kw">assume </span><a NAME="E14:125"/><span class="lab"><font color="Green" title="E76">A9</font></span>: 
<span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><font color="Maroon" title="c8">z</font></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>  <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<font color="Maroon" title="c6">r1</font>,<font color="Maroon" title="c7">r2</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="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font></span><br/>

<a NAME="E15:125"/>
 <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<font color="Maroon" title="c6">r1</font>,<font color="Maroon" title="c7">r2</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">r2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T17" title="XXREAL_0:th.17">XXREAL_0:17</a></span>;<br/>
<a NAME="E16:125"/><span class="kw">then </span>
<span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><font color="Maroon" title="c8">z</font></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> <font color="Maroon" title="c7">r2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:125"><span class="lab"><font color="Green" title="E76">A9</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E17:125"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A10</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:125"><span class="lab"><font color="Green" title="E75">A8</font></span></a></span>;<br/>
<a NAME="E18:125"/>
 <a href="square_1.html#K1" title="SQUARE_1:func.1">min</a> (<font color="Maroon" title="c6">r1</font>,<font color="Maroon" title="c7">r2</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">r1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T17" title="XXREAL_0:th.17">XXREAL_0:17</a></span>;<br/>
<a NAME="E19:125"/><span class="kw">then </span>
<span class="p1"><a href="seq_4.html#K22" title="SEQ_4:func.22">|.</a><span class="default"><font color="Maroon" title="c8">z</font></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> <font color="Maroon" title="c6">r1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:125"><span class="lab"><font color="Green" title="E76">A9</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E20:125"/><span class="kw">then </span>
<font color="Maroon" title="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:125"><span class="lab"><font color="Green" title="E73">A6</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:125"/>
<font color="Maroon" title="c5">x</font> <a href="seq_4.html#K15" title="SEQ_4:func.15">+</a> <font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:125"><span class="lab"><font color="Green" title="E70">A3</font></span></a>, <a class="txt" href="#E17:125"><span class="lab"><font color="Green" title="E77">A10</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</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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