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

<b>set </b><font color="Maroon" title="c5">XN</font> =  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font>;<br/>
<b>set </b><font color="Maroon" title="c6">f</font> =  <a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>;<br/>
<b>set </b><font color="Maroon" title="c7">n</font> =  <a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c8">nextnode</font> =  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="149_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="149_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:149_1_1_1_1"/>
(  not  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> or  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="149_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:149_1_1_1_1_1"/>
not  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> implies  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font> is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ) &amp; (  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> implies  <a href="modelc_3.html#K9" title="MODELC_3:func.9">FinalNode</a> <font color="Maroon" title="c2">v</font> is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> holds  verum ) )</span><br/><div class="add"><b>thus </b><a NAME="E2:149_1_1_1_1_1"/>
( ( not  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> implies  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font> is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ) &amp; (  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> implies  <a href="modelc_3.html#K9" title="MODELC_3:func.9">FinalNode</a> <font color="Maroon" title="c2">v</font> is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> holds  verum ) )
 <b>by </b><i><a class="txt" href="#E1:149"><i><font color="Green" title="E118">A1</font></i></a>, <a class="ref" href="modelc_3.html#D48" target="_self" title="MODELC_3:def.48">DefUsuccEndnum</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="149_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:149_1_1_1_1_2"/>
 <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> implies  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font> is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ) &amp; (  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> implies  <a href="modelc_3.html#K9" title="MODELC_3:func.9">FinalNode</a> <font color="Maroon" title="c2">v</font> is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> holds  verum ) )</span><br/><div class="add"><b>hence </b><a NAME="E2:149_1_1_1_1_2"/>
( ( not  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> implies  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font> is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ) &amp; (  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> implies  <a href="modelc_3.html#K9" title="MODELC_3:func.9">FinalNode</a> <font color="Maroon" title="c2">v</font> is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> holds  verum ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:149_1_1"/>
( ( not  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> implies  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <font color="Maroon" title="c1">w</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">v</font> is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ) &amp; (  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c4">N</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> implies  <a href="modelc_3.html#K9" title="MODELC_3:func.9">FinalNode</a> <font color="Maroon" title="c2">v</font> is  <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a> <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font> holds  verum ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
