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

<span class="kw">let </span><font color="Maroon" title="c1">v</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">N</font> being  <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="c1">v</font><br/> for <font color="Olive" title="b2">w</font> being   <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> <br/> for <font color="Olive" title="b3">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="c1">v</font></span>)</span>  st <font color="Olive" title="b2">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> <font color="Olive" title="b1">N</font> &amp; not <font color="Olive" title="b1">N</font> is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  holds <br/>( <font color="Olive" title="b2">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Olive" title="b2">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Olive" title="b3">U</font>,<font color="Olive" title="b1">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Olive" title="b2">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Olive" title="b3">U</font>,<font color="Olive" title="b1">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Olive" title="b1">N</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">N</font> be   <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="c1">v</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">w</font> being   <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> <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="Maroon" title="c1">v</font></span>)</span>  st <font color="Olive" title="b1">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> <font color="Maroon" title="c2">N</font> &amp; not <font color="Maroon" title="c2">N</font> is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  holds <br/>( <font color="Olive" title="b1">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Olive" title="b1">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Olive" title="b2">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Olive" title="b1">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Olive" title="b2">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="c1">v</font></span>)</span>  st <font color="Maroon" title="c3">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> <font color="Maroon" title="c2">N</font> &amp; not <font color="Maroon" title="c2">N</font> is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  holds <br/>( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Olive" title="b1">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Olive" title="b1">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">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="c1">v</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">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> <font color="Maroon" title="c2">N</font> &amp; not <font color="Maroon" title="c2">N</font> is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  implies ( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> ) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:126"/><span class="lab"><font color="Green" title="E108">A1</font></span>: 
<font color="Maroon" title="c3">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> <font color="Maroon" title="c2">N</font>
 <span class="kw">and </span><br/><a NAME="E2:126"/><span class="lab"><font color="Green" title="E109">A2</font></span>: 
not <font color="Maroon" title="c2">N</font> is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">H</font> =  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">SN</font> =  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">H2</font> =  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>;<br/>
<a NAME="E3:126"/><span class="lab"><font color="Green" title="E110">A3</font></span>: 
 <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:126"><span class="lab"><font color="Green" title="E109">A2</font></span></a>, <a class="ref" href="modelc_3.html#T58" target="_self" title="MODELC_3:th.58">Th58</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:126_1_1"/>
( ( not  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">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#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> ) or (  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#NR9" title="MODELC_2:NR.9">|/=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> ) or ( not <!--HUMANRECFAILED-->( not  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">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#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> ) &amp; not <!--HUMANRECFAILED-->(  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#NR9" title="MODELC_2:NR.9">|/=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> ) ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_1"/><span class="lab"><font color="Green" title="E111">A4</font></span>: 
( ( not  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">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#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> ) or (  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#NR9" title="MODELC_2:NR.9">|/=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )</span><br/><div class="add"><a NAME="E2:126_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E112">A5</font></span>: 
 <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D35" target="_self" title="MODELC_3:def.35">Def35</a></span>;<br/><a NAME="E3:126_1_1_1"/><span class="lab"><font color="Green" title="E113">A6</font></span>: 
<font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:126_1_1_1_1_1_1"/>
( ( not  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">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#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> ) or (  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#NR9" title="MODELC_2:NR.9">|/=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126_1_1_1"><span class="lab"><font color="Green" title="E111">A4</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_1_1_1_1_1"/>
( not  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">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#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:126_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D35" target="_self" title="MODELC_3:def.35">Def35</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E114">A7</font></span>: 
(  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#NR9" title="MODELC_2:NR.9">|/=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c8">N2</font> =  <a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font>;<br/><a NAME="E2:126_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E115">A8</font></span>: 
( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> or <font color="Maroon" title="c3">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#K6" title="MODELC_3:func.6">SuccNode2</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126"><span class="lab"><font color="Green" title="E108">A1</font></span></a>, <a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="txt" href="#E2:126_1_1_1"><span class="lab"><font color="Green" title="E112">A5</font></span></a>, <a class="txt" href="#E1:126_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E114">A7</font></span></a>, <a class="txt" href="modelc_3.html#E42"><span class="lab"><font color="Green" title="E32">Lm19</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_1_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:126_1_1_1_1_1_1_2_1"/>
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/><a NAME="E2:126_1_1_1_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E116">A9</font></span>: 
(  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> implies  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E3:126_1_1_1_1_1_1_2_1"/>
 <a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E114">A7</font></span></a>, <a class="ref" href="modelc_3.html#D2" target="_self" title="MODELC_3:def.2">Def2</a></span>;<br/><a NAME="E4:126_1_1_1_1_1_1_2_1"/><span class="kw">then </span>
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E5:126_1_1_1_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E117">A10</font></span>: 
( not  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> implies  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><span class="kw">assume </span><a NAME="E6:126_1_1_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E118">A11</font></span>: 
not <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E7:126_1_1_1_1_1_1_2_1"/>
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/><a NAME="E8:126_1_1_1_1_1_1_2_1"/><span class="kw">then </span>
( not  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> implies  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:126_1_1_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E117">A10</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E9:126_1_1_1_1_1_1_2_1"/><span class="kw">then </span>
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:126_1_1_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E116">A9</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E10:126_1_1_1_1_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E114">A7</font></span></a>, <a class="txt" href="#E2:126_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E115">A8</font></span></a>, <a class="txt" href="#E6:126_1_1_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E118">A11</font></span></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:126_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:126_1_1_1_1"/>
<font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E4:126_1_1_1"/>
 <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R2" title="MODELC_3:pred.2">is_succ1_of</a> <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="txt" href="#E2:126_1_1_1"><span class="lab"><font color="Green" title="E112">A5</font></span></a>, <a class="ref" href="modelc_3.html#D7" target="_self" title="MODELC_3:def.7">Def7</a></span>;<br/><span class="kw">hence </span><a NAME="E5:126_1_1_1"/>
( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:126_1_1_1"><span class="lab"><font color="Green" title="E113">A6</font></span></a>, <a class="ref" href="modelc_3.html#D9" target="_self" title="MODELC_3:def.9">Def9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_2"/><span class="lab"><font color="Green" title="E111">A12</font></span>: 
( not <!--HUMANRECFAILED-->( not  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">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#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> ) &amp; not <!--HUMANRECFAILED-->(  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#NR9" title="MODELC_2:NR.9">|/=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c8">N1</font> =  <a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font>;<br/><a NAME="E2:126_1_1_2"/><span class="lab"><font color="Green" title="E112">A13</font></span>: 
 <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126_1_1_2"><span class="lab"><font color="Green" title="E111">A12</font></span></a>, <a class="ref" href="modelc_3.html#D35" target="_self" title="MODELC_3:def.35">Def35</a></span>;<br/><a NAME="E3:126_1_1_2"/>
( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_2_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:126_1_1_2_1_1_1"/>
( (  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> ) or  not <font color="Maroon" title="c3">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#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126_1_1_2"><span class="lab"><font color="Green" title="E111">A12</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_2_1_1_1_1"/><span class="lab"><font color="Green" title="E113">A14</font></span>: 
(  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  &amp; <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c9">NN</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font>;<br/><span class="kw">set </span><font color="Maroon" title="c10">NO</font> = the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font>;<br/><span class="kw">set </span><font color="Maroon" title="c11">SNN</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>;<br/><a NAME="E2:126_1_1_2_1_1_1_1"/>
 <a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E113">A14</font></span></a>, <a class="ref" href="modelc_3.html#D2" target="_self" title="MODELC_3:def.2">Def2</a></span>;<br/><a NAME="E3:126_1_1_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E114">A15</font></span>: 
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="txt" href="#E2:126_1_1_2"><span class="lab"><font color="Green" title="E112">A13</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/><a NAME="E4:126_1_1_2_1_1_1_1"/>
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></span>;<br/><a NAME="E5:126_1_1_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E115">A16</font></span>: 
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:126_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E114">A15</font></span></a>, <a class="ref" href="xboole_1.html#T13" title="XBOOLE_1:th.13">XBOOLE_1:13</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c12">NX</font> = the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N</font>;<br/><span class="kw">set </span><font color="Maroon" title="c13">SNX</font> = the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c14">SNO</font> = the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>;<br/><a NAME="E6:126_1_1_2_1_1_1_1"/>
( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="txt" href="#E2:126_1_1_2"><span class="lab"><font color="Green" title="E112">A13</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></span>;<br/><a NAME="E7:126_1_1_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E116">A17</font></span>: 
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></span>;<br/><a NAME="E8:126_1_1_2_1_1_1_1"/><span class="lab"><font color="Green" title="E117">A18</font></span>: 
the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="txt" href="#E2:126_1_1_2"><span class="lab"><font color="Green" title="E112">A13</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/><a NAME="E9:126_1_1_2_1_1_1_1"/><span class="lab"><font color="Green" title="E118">A19</font></span>: 
for <font color="Olive" title="b1">G</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st <font color="Olive" title="b1">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> holds <br/><font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Olive" title="b1">G</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_2_1_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c15">G</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> implies <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c15">G</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:126_1_1_2_1_1_1_1_1"/><span class="lab"><font color="Green" title="E119">A20</font></span>: 
<font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c15">G</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_2_1_1_1_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2_1_1_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:126_1_1_2_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> or <font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> or <font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126_1_1_2_1_1_1_1_1"><span class="lab"><font color="Green" title="E119">A20</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2_1_1_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_2_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c15">G</font></span><br/><div class="add"><a NAME="E2:126_1_1_2_1_1_1_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:126_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E116">A17</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:126_1_1_2_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c15">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126"><span class="lab"><font color="Green" title="E108">A1</font></span></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2_1_1_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_2_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c15">G</font></span><br/><div class="add"><a NAME="E2:126_1_1_2_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N</font> or <font color="Maroon" title="c15">G</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"><span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:126_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E115">A16</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E3:126_1_1_2_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c2">N</font> or <font color="Maroon" title="c15">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:126_1_1_2_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c15">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126"><span class="lab"><font color="Green" title="E108">A1</font></span></a>, <a class="txt" href="#E1:126_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E113">A14</font></span></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2_1_1_1_1_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_2_1_1_1_1_1_1_1_3"/>
<font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c15">G</font></span><br/><div class="add"><a NAME="E2:126_1_1_2_1_1_1_1_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c15">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:126_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E117">A18</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:126_1_1_2_1_1_1_1_1_1_1_3"/>
<font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c15">G</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126"><span class="lab"><font color="Green" title="E108">A1</font></span></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:126_1_1_2_1_1_1_1_1"/>
<font color="Maroon" title="c3">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c15">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E10:126_1_1_2_1_1_1_1"/>
 <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R3" title="MODELC_3:pred.3">is_succ2_of</a> <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="txt" href="#E2:126_1_1_2"><span class="lab"><font color="Green" title="E112">A13</font></span></a>, <a class="txt" href="#E1:126_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E113">A14</font></span></a>, <a class="ref" href="modelc_3.html#D8" target="_self" title="MODELC_3:def.8">Def8</a></span>;<br/><span class="kw">hence </span><a NAME="E11:126_1_1_2_1_1_1_1"/>
( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:126_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E118">A19</font></span></a>, <a class="ref" href="modelc_3.html#D9" target="_self" title="MODELC_3:def.9">Def9</a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_2_1_1_1_2"/><span class="lab"><font color="Green" title="E113">A21</font></span>: 
not <font color="Maroon" title="c3">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#K5" title="MODELC_3:func.5">SuccNode1</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span>,<font color="Maroon" title="c2">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )</span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_2_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2_1_1_1_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:126_1_1_2_1_1_1_2_1_1"/>
(  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T2" title="MODELC_2:th.2">MODELC_2:2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2_1_1_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_2_1_1_1_2_1_1_1"/>
(  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V2" title="MODELC_2:attr.2">atomic</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V3" title="MODELC_2:attr.3">negative</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V4" title="MODELC_2:attr.4">conjunctive</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:126_1_1_2_1_1_1_2_1_1_1"/>
( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126"><span class="lab"><font color="Green" title="E108">A1</font></span></a>, <a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="txt" href="#E1:126_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E113">A21</font></span></a>, <a class="txt" href="modelc_3.html#E38"><span class="lab"><font color="Green" title="E29">Lm16</font></span></a>, <a class="txt" href="modelc_3.html#E39"><span class="lab"><font color="Green" title="E30">Lm17</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="126_1_1_2_1_1_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:126_1_1_2_1_1_1_2_1_1_2"/><span class="lab"><font color="Green" title="E114">A22</font></span>: 
(  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  or  <a href="modelc_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )</span><br/><div class="add"><a NAME="E2:126_1_1_2_1_1_1_2_1_1_2"/><span class="kw">then </span>
 <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R3" title="MODELC_3:pred.3">is_succ2_of</a> <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="txt" href="#E2:126_1_1_2"><span class="lab"><font color="Green" title="E112">A13</font></span></a>, <a class="ref" href="modelc_3.html#D8" target="_self" title="MODELC_3:def.8">Def8</a></span>;<br/><span class="kw">hence </span><a NAME="E3:126_1_1_2_1_1_1_2_1_1_2"/>
( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:126"><span class="lab"><font color="Green" title="E108">A1</font></span></a>, <a class="txt" href="#E3:126"><span class="lab"><font color="Green" title="E110">A3</font></span></a>, <a class="txt" href="#E2:126_1_1_2"><span class="lab"><font color="Green" title="E112">A13</font></span></a>, <a class="txt" href="#E1:126_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E113">A21</font></span></a>, <a class="txt" href="#E1:126_1_1_2_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E114">A22</font></span></a>, <a class="ref" href="modelc_3.html#D9" target="_self" title="MODELC_3:def.9">Def9</a>, <a class="txt" href="modelc_3.html#E41"><span class="lab"><font color="Green" title="E31">Lm18</font></span></a>, <a class="txt" href="modelc_3.html#E42"><span class="lab"><font color="Green" title="E32">Lm19</font></span></a>, <a class="txt" href="modelc_3.html#E43"><span class="lab"><font color="Green" title="E33">Lm20</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:126_1_1_2_1_1_1_2"/>
( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:126_1_1_2_1"/>
( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:126_1_1_2"/>
( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:126"/>
( <font color="Maroon" title="c3">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#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font></span>)</span> &amp;  <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c2">N</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c2">N</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
