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<a NAME="E1:148_1_1"/><span class="lab"><font color="Green" title="E119">A3</font></span>: 
<font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<font color="Maroon" title="c4">N</font>,<font color="Maroon" title="c2">v</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:148"><span class="lab"><font color="Green" title="E118">A2</font></span></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">Def16</a></span>;<br/>
<a NAME="E2:148_1_1"/>
( <font color="Maroon" title="c4">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c2">v</font> &amp;  not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<font color="Maroon" title="c4">N</font>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:148"><span class="lab"><font color="Green" title="E117">A1</font></span></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">Def16</a>, <a class="ref" href="modelc_3.html#D30" target="_self" title="MODELC_3:def.30">Def30</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:148_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( (  for <font color="Olive" title="b2">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b2">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive">b<sub>1</sub></font> holds <br/>(  not  <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#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  &amp;  <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#K30" title="MODELC_1:func.30">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) ) ) &amp;  <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#K30" title="MODELC_1:func.30">|**</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>) is  <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>  &amp; (  for <font color="Olive" title="b2">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b2">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon" title="c1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<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#K30" title="MODELC_1:func.30">|**</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">N</font></span>)</span>,<font color="Maroon" title="c2">v</font>)</span>)</span> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:148_1_1"><span class="lab"><font color="Green" title="E119">A3</font></span></a>, <a class="ref" href="modelc_3.html#T51" target="_self" title="MODELC_3:th.51">Th51</a>, <a class="ref" href="modelc_3.html#T62" target="_self" title="MODELC_3:th.62">Th62</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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