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

<b>let </b><font color="Maroon" title="c1">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">v</font> being <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><br/> for <font color="Olive" title="b2">U</font> being   <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="orders_1.html#K1" title="ORDERS_1:func.1">BOOL</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Olive" title="b1">v</font></span>)</span>  st <font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Olive" title="b1">v</font> holds <br/>for <font color="Olive" title="b3">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds <br/> (  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Olive" title="b1">v</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">n</font></span>)</span>,<font color="Olive" title="b1">v</font> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Olive" title="b3">n</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">n</font></span>)</span>,<font color="Olive" title="b1">v</font></span>)</span></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c2">v</font> be  <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">U</font> being   <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="orders_1.html#K1" title="ORDERS_1:func.1">BOOL</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">v</font></span>)</span>  st <font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">v</font> holds <br/>for <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds <br/> (  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">n</font></span>)</span>,<font color="Maroon" title="c2">v</font> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Olive" title="b2">n</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">n</font></span>)</span>,<font color="Maroon" title="c2">v</font></span>)</span></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c3">U</font> be    <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="orders_1.html#K1" title="ORDERS_1:func.1">BOOL</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c2">v</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">v</font> implies for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds <br/> (  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Maroon" title="c2">v</font> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Olive" title="b1">n</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Maroon" title="c2">v</font></span>)</span></span>)</span> ) )</span><br/>





<b>set </b><font color="Maroon" title="c4">s</font> =  <a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font>;<br/>
<b>assume </b><a NAME="E1:156"/>
<font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c2">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds <br/> (  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Maroon" title="c2">v</font> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Olive" title="b1">n</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Maroon" title="c2">v</font></span>)</span></span>)</span> )</span><br/>

<a NAME="E2:156"/><b>then </b><i><font color="Green" title="E125">A1</font></i>: 
<font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="modelc_3.html#T72" target="_self" title="MODELC_3:th.72">thBA04</a></i>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>) <b>-&gt; </b> <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> =  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1</span>)</span>,<font color="Maroon" title="c2">v</font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b>( <font color="Maroon">H<sub>1</sub></font>($1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1) <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Maroon">H<sub>1</sub></font>($1) &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,$1 <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon">H<sub>1</sub></font>($1)</span>)</span> );<br/>
<a NAME="E3:156"/><i><font color="Green" title="E126">A2</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="156_1"><b>proof </b></a><div class="add">

<i><font color="Green" title="E127">B0</font></i>:  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c2">v</font> = 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font></span>)</span>,<font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D50" target="_self" title="MODELC_3:def.50">Defchosenrun</a></i>
<br/>.= 
 <a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>
;<br/>
<font color="Maroon">H<sub>1</sub></font>(<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1) = 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c2">v</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D50" target="_self" title="MODELC_3:def.50">Defchosenrun</a></i>
<br/>.= 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="txt" href="#E1:156_1"><i><font color="Green" title="E127">B0</font></i></a>, <a class="ref" href="modelc_2.html#T79" title="MODELC_2:th.79">MODELC_2:79</a></i>
<br/>.= 
 <a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p1">(<span class="default"><a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font></span>)</span>
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>
;<br/>
<b>hence </b><a NAME="E3:156_1"/>
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 <b>by </b><i><a class="txt" href="#E1:156_1"><i><font color="Green" title="E127">B0</font></i></a>, <a class="ref" href="modelc_3.html#T69" target="_self" title="MODELC_3:th.69">thChoicedNext01</a>, <a class="txt" href="#E2:156"><i><font color="Green" title="E125">A1</font></i></a>, <a class="ref" href="modelc_2.html#T79" title="MODELC_2:th.79">MODELC_2:79</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>
<a NAME="E4:156"/><i><font color="Green" title="E127">A3</font></i>: 
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="156_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">n</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<b>set </b><font color="Maroon" title="c6">n1</font> = <font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/>
<b>set </b><font color="Maroon" title="c7">w1</font> =  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c5">n</font>;<br/>
<b>set </b><font color="Maroon" title="c8">w2</font> =  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>;<br/>
<a NAME="E1:156_2"/><i><font color="Green" title="E128">B0</font></i>: 
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c5">n</font></span>)</span>,1
 
<b>by </b><i><a class="ref" href="modelc_2.html#T80" title="MODELC_2:th.80">MODELC_2:80</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">s1</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>);<br/>
<b>set </b><font color="Maroon" title="c10">s2</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1);<br/>
<b>set </b><font color="Maroon" title="c11">s3</font> = <font color="Maroon">H<sub>1</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1);<br/>
<a NAME="E2:156_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="156_2_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="156_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="156_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:156_2_1_1_1"/>
( <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <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="c5">n</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="156_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:156_2_1_1_1_1"/>
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font></span><br/><div class="add"><b>then </b><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) = 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font></span>)</span>,<font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D50" target="_self" title="MODELC_3:def.50">Defchosenrun</a></i>
<br/>.= 
 <a href="modelc_3.html#K11" title="MODELC_3:func.11">init</a> <font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>
;<br/><b>hence </b><a NAME="E3:156_2_1_1_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font>
 ; <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="156_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:156_2_1_1_1_2"/><i><font color="Green" title="E129">C1</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="c5">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c12">m</font> = <font color="Maroon" title="c5">n</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1;<br/><b>reconsider </b><font color="Maroon" title="c13">m</font> = <font color="Maroon" title="c5">n</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <b>by </b><i><a class="txt" href="#E1:156_2_1_1_1_2"><i><font color="Green" title="E129">C1</font></i></a>, <a class="ref" href="nat_1.html#T20" title="NAT_1:th.20">NAT_1:20</a></i>;<br/><a NAME="E3:156_2_1_1_1_2"/><i><font color="Green" title="E130">D1</font></i>: 
<font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ;<br/><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) = 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c13">m</font></span>)</span>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">m</font></span>)</span>,<font color="Maroon" title="c2">v</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D50" target="_self" title="MODELC_3:def.50">Defchosenrun</a>, <a class="txt" href="#E3:156_2_1_1_1_2"><i><font color="Green" title="E130">D1</font></i></a></i>
<br/>.= 
 <a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c13">m</font></span>)</span>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">m</font></span>)</span>,<font color="Maroon" title="c2">v</font></span>)</span>
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>
;<br/><b>hence </b><a NAME="E5:156_2_1_1_1_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font>
 ; <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></div><b>end;</b></div>
<b>hence </b><a NAME="E2:156_2_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font>
 ; <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>then reconsider </b><font color="Maroon" title="c12">s1</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font>) as  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ;<br/>
<i><font color="Green" title="E129">B02</font></i>: <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1) = 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c5">n</font></span>)</span>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span>)</span>,<font color="Maroon" title="c2">v</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D50" target="_self" title="MODELC_3:def.50">Defchosenrun</a></i>
<br/>.= 
 <a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c5">n</font></span>)</span>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<font color="Maroon" title="c12">s1</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon" title="c13">s2</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1) as  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ;<br/>
<i><font color="Green" title="E130">B03</font></i>: <font color="Maroon">H<sub>1</sub></font>(<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1) = 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D50" target="_self" title="MODELC_3:def.50">Defchosenrun</a></i>
<br/>.= 
 <a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<font color="Maroon" title="c13">s2</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>
;<br/>
<b>assume </b><a NAME="E7:156_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">n</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<a NAME="E8:156_2"/><b>then </b><i><font color="Green" title="E131">B3</font></i>: 
(  <a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c5">n</font></span>)</span>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<font color="Maroon" title="c12">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Maroon" title="c12">s1</font> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c5">n</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c5">n</font></span>)</span>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<font color="Maroon" title="c12">s1</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="modelc_3.html#T69" target="_self" title="MODELC_3:th.69">thChoicedNext01</a></i>;<br/>
<a NAME="E9:156_2"/>
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c13">s2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:156_2"><i><font color="Green" title="E128">B0</font></i></a>, <a class="txt" href="#E8:156_2"><i><font color="Green" title="E131">B3</font></i></a>, <a class="txt" href="#E4:156_2"><i><font color="Green" title="E129">B02</font></i></a>, <a class="ref" href="modelc_3.html#T70" target="_self" title="MODELC_3:th.70">thBA02</a></i>;<br/>
<b>hence </b><a NAME="E10:156_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 <b>by </b><i><a class="ref" href="modelc_3.html#T69" target="_self" title="MODELC_3:th.69">thChoicedNext01</a>, <a class="txt" href="#E6:156_2"><i><font color="Green" title="E130">B03</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>
<a NAME="E5:156"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="#E3:156"><i><font color="Green" title="E126">A2</font></i></a>, <a class="txt" href="#E4:156"><i><font color="Green" title="E127">A3</font></i></a>);<br/></i>
<b>hence </b><a NAME="E6:156"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds <br/> (  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Maroon" title="c2">v</font> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c1">w</font>,<font color="Olive" title="b1">n</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Maroon" title="c2">v</font></span>)</span></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
