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

<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">F</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">D</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c3">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E11">A1</font></i>: 
 <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="c3">r</font>
 ;<br/>

<a NAME="E2:12"/><i><font color="Green" title="E12">A2</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">F</font>
 
<b>by </b><i><a class="ref" href="seq_1.html#D10" title="SEQ_1:def.10">SEQ_1:def 10</a></i>;<br/>
<b>thus </b><a NAME="E3:12"/>
<span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><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="c3">r</font></span>)</span>,<font color="Maroon" title="c3">r</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">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="E1:12_1"/><i><font color="Green" title="E13">A3</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">rr</font> = <font color="Maroon" title="c4">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> ;<br/>
<a NAME="E3:12_1"/><i><font color="Green" title="E14">A4</font></i>: 
( <font color="Maroon" title="c5">rr</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> <span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="txt" href="rfunct_3.html#E1:12_1"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></i>;<br/>
<a NAME="E4:12_1"/><b>then </b>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="seq_1.html#D10" title="SEQ_1:def.10">SEQ_1:def 10</a></i>;<br/>
<a NAME="E5:12_1"/><b>then </b><i><font color="Green" title="E15">A5</font></i>: 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:12_1_1_1"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> or <font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1_1_1"><b>case </b></a><a NAME="E1:12_1_1_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font>
 ;<br/><div class="add"><a NAME="E2:12_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font>
 <b>by </b><i><a class="txt" href="rfunct_3.html#E5:12_1"><i><font color="Green" title="E15">A5</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>;<br/><a NAME="E3:12_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><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="c3">r</font></span>)</span>,<font color="Maroon" title="c3">r</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E4:12_1_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><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="c3">r</font></span>)</span>,<font color="Maroon" title="c3">r</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="rfunct_3.html#E2:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="rfunct_3.html#E3:12_1"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1_1_2"><b>case </b></a><a NAME="E1:12_1_1_1_2"/>
<font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><a NAME="E2:12_1_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="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font>
 <b>by </b><i><a class="txt" href="rfunct_3.html#E5:12_1"><i><font color="Green" title="E15">A5</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>;<br/><a NAME="E3:12_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><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="c3">r</font></span>)</span>,<font color="Maroon" title="c3">r</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E4:12_1_1_1_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><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="c3">r</font></span>)</span>,<font color="Maroon" title="c3">r</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="txt" href="rfunct_3.html#E2:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="rfunct_3.html#E3:12_1"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:12_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><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="c3">r</font></span>)</span>,<font color="Maroon" title="c3">r</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c4">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="E4:12"/><i><font color="Green" title="E13">A6</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><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="c3">r</font></span>)</span>,<font color="Maroon" title="c3">r</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">rr</font> = <font color="Maroon" title="c4">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">D</font> ;<br/>
<a NAME="E6:12"/><i><font color="Green" title="E14">A7</font></i>: 
( <font color="Maroon" title="c5">rr</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">F</font> &amp; <font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><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="c3">r</font></span>)</span>,<font color="Maroon" title="c3">r</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="txt" href="rfunct_3.html#E4:12"><i><font color="Green" title="E13">A6</font></i></a>, <a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:12_2_1"/>
( <font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">r</font> or <font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font> )
 </span><b>by </b><i><a class="txt" href="rfunct_3.html#E6:12"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_2_1_1"><b>case </b></a><a NAME="E1:12_2_1_1"/>
<font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c3">r</font>
 ;<br/><div class="add"><b>then </b><font color="Maroon" title="c3">r</font> = 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</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"><font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_3.html#E1:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>
<br/>.= 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font></span>)</span>
<b>by </b><i><a class="ref" href="complex1.html#T138" title="COMPLEX1:th.138">COMPLEX1:138</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font>
<b>by </b><i><a class="txt" href="rfunct_3.html#E2:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="rfunct_3.html#E6:12"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="seq_1.html#D10" title="SEQ_1:def.10">SEQ_1:def 10</a></i>
;<br/><a NAME="E3:12_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:12_2_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="rfunct_3.html#E2:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="rfunct_3.html#E6:12"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_2_1_2"><b>case </b></a><a NAME="E1:12_2_1_2"/>
<font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">r</font>
 ;<br/><div class="add"><b>then </b><font color="Maroon" title="c3">r</font> = 
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">F</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_3.html#E1:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font>
<b>by </b><i><a class="txt" href="rfunct_3.html#E2:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="rfunct_3.html#E6:12"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="seq_1.html#D10" title="SEQ_1:def.10">SEQ_1:def 10</a></i>
;<br/><a NAME="E3:12_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">rr</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:12_2_1_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="rfunct_3.html#E2:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="txt" href="rfunct_3.html#E6:12"><i><font color="Green" title="E14">A7</font></i></a>, <a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E8:12"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">r</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ;<br/>


</div>
