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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="membered.html#V2" title="MEMBERED:attr.2">ext-real-membered</a> non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> non <a href="xxreal_2.html#V1" title="XXREAL_2:attr.1">left_end</a> non <a href="xxreal_2.html#V2" title="XXREAL_2:attr.2">right_end</a> <a href="xxreal_2.html#V6" title="XXREAL_2:attr.6">connected</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span></span><br/><b>let </b><font color="Maroon" title="c2">x</font> be  <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="membered.html#D14" title="MEMBERED:def.14">MEMBERED:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> ) &amp; (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> ) )</span><br/>



<b>thus </b><a NAME="E1:129"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> implies <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="129_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:129_1"/><i><font color="Green" title="E74">Z</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span></span><br/>

<a NAME="E2:129_1"/><b>then </b><i><font color="Green" title="E75">A</font></i>: 
 <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="ref" href="xxreal_2.html#T3" target="_self" title="XXREAL_2:th.3">Th3</a></i>;<br/>
<a NAME="E3:129_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="#E1:129_1"><i><font color="Green" title="E74">Z</font></i></a>, <a class="ref" href="xxreal_2.html#D5" target="_self" title="XXREAL_2:def.5">Def5</a></i>;<br/>
<a NAME="E4:129_1"/><b>then </b><i><font color="Green" title="E76">C</font></i>: 
 <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="txt" href="#E2:129_1"><i><font color="Green" title="E75">A</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>
<a NAME="E5:129_1"/><i><font color="Green" title="E77">B</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="#E1:129_1"><i><font color="Green" title="E74">Z</font></i></a>, <a class="ref" href="xxreal_2.html#T4" target="_self" title="XXREAL_2:th.4">Th3B</a></i>;<br/>
<a NAME="E6:129_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="#E1:129_1"><i><font color="Green" title="E74">Z</font></i></a>, <a class="ref" href="xxreal_2.html#D6" target="_self" title="XXREAL_2:def.6">Def6</a></i>;<br/>
<a NAME="E7:129_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="#E5:129_1"><i><font color="Green" title="E77">B</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>
<b>hence </b><a NAME="E8:129_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span>
 <b>by </b><i><a class="txt" href="#E4:129_1"><i><font color="Green" title="E76">C</font></i></a>, <a class="ref" href="xxreal_1.html#T4" title="XXREAL_1:th.4">XXREAL_1:4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>assume </b><a NAME="E2:129"/><i><font color="Green" title="E74">Z</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font></span><br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[ <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ] <b>means </b>( $1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> &amp; $1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">x</font> );<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[ <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ] <b>means </b>( $1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> &amp; $1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c2">x</font> );<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="129_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:129_2"/>
( for <font color="Olive" title="b1">r</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   holds  not <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>] or for <font color="Olive" title="b1">r</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   holds  not <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">r</font>] or (  ex <font color="Olive" title="b1">r</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>] &amp;  ex <font color="Olive" title="b1">r</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">r</font>] ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="129_2_1"><b>suppose </b></a><a NAME="E1:129_2_1"/>
for <font color="Olive" title="b1">r</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   holds  not <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font></span><br/><div class="add"><a NAME="E2:129_2_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> is    <a href="xxreal_2.html#M2" title="XXREAL_2:mode.2">LowerBound</a> of <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="xxreal_2.html#D2" target="_self" title="XXREAL_2:def.2">Def2</a></i>;<br/><a NAME="E3:129_2_1"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="xxreal_2.html#D4" target="_self" title="XXREAL_2:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E4:129_2_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="#E2:129"><i><font color="Green" title="E74">Z</font></i></a>, <a class="ref" href="xxreal_1.html#T4" title="XXREAL_1:th.4">XXREAL_1:4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="129_2_2"><b>suppose </b></a><a NAME="E1:129_2_2"/>
for <font color="Olive" title="b1">r</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   holds  not <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">r</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font></span><br/><div class="add"><a NAME="E2:129_2_2"/><b>then </b>
<font color="Maroon" title="c2">x</font> is    <a href="xxreal_2.html#M1" title="XXREAL_2:mode.1">UpperBound</a> of <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="xxreal_2.html#D1" target="_self" title="XXREAL_2:def.1">Def1</a></i>;<br/><a NAME="E3:129_2_2"/><b>then </b>
 <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <font color="Maroon" title="c1">A</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="ref" href="xxreal_2.html#D3" target="_self" title="XXREAL_2:def.3">Def3</a></i>;<br/><b>hence </b><a NAME="E4:129_2_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="#E2:129"><i><font color="Green" title="E74">Z</font></i></a>, <a class="ref" href="xxreal_1.html#T4" title="XXREAL_1:th.4">XXREAL_1:4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="129_2_3"><b>suppose </b></a><b>that </b><a NAME="E1:129_2_3"/><i><font color="Green" title="E75">S1</font></i>: 
 ex <font color="Olive" title="b1">r</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">r</font>]
 <b>and </b><br/><a NAME="E2:129_2_3"/><i><font color="Green" title="E76">S2</font></i>: 
 ex <font color="Olive" title="b1">r</font> being <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>  st <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">r</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font></span><br/><div class="add"><b>consider </b><font color="Maroon" title="c3">r</font> being  <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E4:129_2_3"/><i><font color="Green" title="E77">W3</font></i>: 
<font color="Maroon" title="c3">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>and </b><br/><a NAME="E5:129_2_3"/><i><font color="Green" title="E78">W4</font></i>: 
<font color="Maroon" title="c3">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="txt" href="#E1:129_2_3"><i><font color="Green" title="E75">S1</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c4">s</font> being  <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E7:129_2_3"/><i><font color="Green" title="E79">W5</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>and </b><br/><a NAME="E8:129_2_3"/><i><font color="Green" title="E80">W6</font></i>: 
<font color="Maroon" title="c4">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="txt" href="#E2:129_2_3"><i><font color="Green" title="E76">S2</font></i></a></i>;<br/><a NAME="E9:129_2_3"/><i><font color="Green" title="E81">A</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K1" title="XXREAL_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">s</font></span><a href="xxreal_1.html#K1" title="XXREAL_1:func.1">.]</a></span>
 <b>by </b><i><a class="txt" href="#E5:129_2_3"><i><font color="Green" title="E78">W4</font></i></a>, <a class="txt" href="#E8:129_2_3"><i><font color="Green" title="E80">W6</font></i></a>, <a class="ref" href="xxreal_1.html#T1" title="XXREAL_1:th.1">XXREAL_1:1</a></i>;<br/><a NAME="E10:129_2_3"/>
<span class="p1"><a href="xxreal_1.html#K1" title="XXREAL_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">r</font>,<font color="Maroon" title="c4">s</font></span><a href="xxreal_1.html#K1" title="XXREAL_1:func.1">.]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="#E4:129_2_3"><i><font color="Green" title="E77">W3</font></i></a>, <a class="txt" href="#E7:129_2_3"><i><font color="Green" title="E79">W5</font></i></a>, <a class="ref" href="xxreal_2.html#D12" target="_self" title="XXREAL_2:def.12">Def12</a></i>;<br/><b>hence </b><a NAME="E11:129_2_3"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="#E9:129_2_3"><i><font color="Green" title="E81">A</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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