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

<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S1</font>) <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  =  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s1</font>)</span>)</span> where <font color="Olive" title="b1">s1</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> $1 </span> } </span> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c3">f</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E2:22_1_1"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> &amp; (  for <font color="Olive" title="b1">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S1</font> holds  <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">d</font>) ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_1.html#S4" onmouseover="rs('funct_1/S4')" onmouseout="rh()">FUNCT_1:sch 4</a>();<br/></span>
<span class="kw">reconsider </span><font color="Maroon" title="c4">f</font> = <font color="Maroon" title="c3">f</font> as   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a>, <a class="ref" href="relat_1.html#D18" onmouseover="rs('relat_1/D18')" onmouseout="rh()">RELAT_1:def 18</a></span>;<br/>
<a NAME="E4:22_1_1"/>
<font color="Maroon" title="c4">f</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">OU0</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">s</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="pboole.html#D2" onmouseover="rs('pboole/D2')" onmouseout="rh()">PBOOLE:def 2</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> or <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">OU0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:22_1_1_1"/>
<font color="Maroon" title="c5">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">OU0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">s1</font> = <font color="Maroon" title="c5">s</font> as   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> ;<br/>
<a NAME="E3:22_1_1_1"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_2.html#K1" title="OSALG_2:func.1">OSConstants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Maroon" title="c6">s1</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:22_1_1_1"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">OU0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">f</font> = <font color="Maroon" title="c4">f</font> as   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">OU0</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D18" onmouseover="rs('pboole/D18')" onmouseout="rh()">PBOOLE:def 18</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">f</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">f</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">OU0</font> &amp; (  for <font color="Olive" title="b1">s</font> being   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> holds  <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_2.html#K1" title="OSALG_2:func.1">OSConstants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s</font>) ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">f1</font> = <font color="Maroon" title="c5">f</font> as   <a href="struct_0.html#NM8" title="STRUCT_0:NM.8">ManySortedSet</a> of <font color="Maroon" title="c1">S1</font> ;<br/>
<a NAME="E7:22_1_1"/>
<font color="Maroon" title="c6">f1</font> is  <a href="osalg_1.html#V11" title="OSALG_1:attr.11">order-sorted</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="22_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">r1</font>, <font color="Maroon" title="c8">r2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S1</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="osalg_1.html#D16" onmouseover="rs('osalg_1/D16')" onmouseout="rh()">OSALG_1:def 16</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">r1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">r2</font> or <font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">r1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">r2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:22_1_1_2"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
<font color="Maroon" title="c7">r1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">r2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">r1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">r2</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">r1</font> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">r2</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:22_1_1_2"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">r1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">r2</font></span><br/>

<a NAME="E3:22_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s2</font>)</span>)</span> where <font color="Olive" title="b1">s2</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">r1</font> </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <span class="kw"> such that </span><br/><a NAME="E5:22_1_1_2"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
( <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">y</font> &amp; <font color="Maroon" title="c10">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s2</font>)</span>)</span> where <font color="Olive" title="b1">s2</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">r1</font> </span> } </span>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D4" onmouseover="rs('tarski/D4')" onmouseout="rh()">TARSKI:def 4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">s3</font> being   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font><span class="kw"> such that </span><br/><a NAME="E7:22_1_1_2"/><span class="lab"><font color="Green" title="E15">A4</font></span>: 
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Maroon" title="c11">s3</font>)
 <span class="kw">and </span><br/><a NAME="E8:22_1_1_2"/><span class="lab"><font color="Green" title="E16">A5</font></span>: 
<font color="Maroon" title="c11">s3</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">r1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22_1_1_2"><span class="lab"><font color="Green" title="E14">A3</font></span></a></span>;<br/>
<a NAME="E9:22_1_1_2"/>
<font color="Maroon" title="c11">s3</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">r2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1_2"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E8:22_1_1_2"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/>
<a NAME="E10:22_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s2</font>)</span>)</span> where <font color="Olive" title="b1">s2</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">r2</font> </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:22_1_1_2"><span class="lab"><font color="Green" title="E15">A4</font></span></a></span>;<br/>
<a NAME="E11:22_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="msualg_2.html#K1" title="MSUALG_2:func.1">Constants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s2</font>)</span>)</span> where <font color="Olive" title="b1">s2</font> is   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> : <font color="Olive" title="b1">s2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">r2</font> </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22_1_1_2"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="tarski.html#D4" onmouseover="rs('tarski/D4')" onmouseout="rh()">TARSKI:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:22_1_1_2"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">r2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E8:22_1_1"/>
<font color="Maroon" title="c5">f</font> is    <a href="osalg_2.html#M2" title="OSALG_2:mode.2">OSSubset</a> of <font color="Maroon" title="c2">OU0</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_2.html#D2" target="_self" onmouseover="rs('osalg_2/D2')" onmouseout="rh()">Def2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> holds  <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_2.html#K1" title="OSALG_2:func.1">OSConstants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s</font>)</span><br/>

<span class="kw">thus </span><a NAME="E9:22_1_1"/>
 for <font color="Olive" title="b1">s</font> being   <a href="osalg_1.html#NM1" title="OSALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S1</font> holds  <font color="Maroon" title="c5">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_2.html#K1" title="OSALG_2:func.1">OSConstants</a> (<font color="Maroon" title="c2">OU0</font>,<font color="Olive" title="b1">s</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E12">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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