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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font>, <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font>  st <font color="Olive" title="b2">f</font> <a href="modelc_3.html#R7" title="MODELC_3:pred.7">is_succ_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Olive" title="b1">w</font> holds <br/>for <font color="Olive" title="b3">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b3">x</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="c1">v</font> &amp; not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Olive" title="b3">x</font>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> &amp; <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#K10" title="MODELC_3:func.10">CastNode</a> <font color="Olive" title="b3">x</font>,<font color="Maroon" title="c1">v</font></span>)</span> holds <br/>for <font color="Olive" title="b4">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( for <font color="Olive" title="b5">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b5">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">k</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"><font color="Olive" title="b2">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b5">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> ) holds <br/>(  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b4">k</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="Olive" title="b3">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Olive" title="b2">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b4">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b4">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c2">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font>, <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font>  st <font color="Olive" title="b1">f</font> <a href="modelc_3.html#R7" title="MODELC_3:pred.7">is_succ_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font> holds <br/>for <font color="Olive" title="b2">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">x</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="c1">v</font> &amp; not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Olive" title="b2">x</font>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> &amp; <font color="Maroon" title="c2">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="Olive" title="b2">x</font>,<font color="Maroon" title="c1">v</font></span>)</span> holds <br/>for <font color="Olive" title="b3">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( for <font color="Olive" title="b4">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b4">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">k</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"><font color="Olive" title="b1">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b4">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> ) holds <br/>(  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">k</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="Olive" title="b2">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Olive" title="b1">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Olive" title="b1">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b3">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )</span><br/>



<b>set </b><font color="Maroon" title="c3">LN</font> =  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font>;<br/>
<b>let </b><font color="Maroon" title="c4">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font>, <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c1">v</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">f</font> <a href="modelc_3.html#R7" title="MODELC_3:pred.7">is_succ_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font> implies for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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="c1">v</font> &amp; not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> &amp; <font color="Maroon" title="c2">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="Olive" title="b1">x</font>,<font color="Maroon" title="c1">v</font></span>)</span> holds <br/>for <font color="Olive" title="b2">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( for <font color="Olive" title="b3">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> ) holds <br/>(  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> ) )</span><br/>

<b>assume </b><a NAME="E1:110"/><i><font color="Green" title="E95">A1</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="modelc_3.html#R7" title="MODELC_3:pred.7">is_succ_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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="c1">v</font> &amp; not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> &amp; <font color="Maroon" title="c2">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="Olive" title="b1">x</font>,<font color="Maroon" title="c1">v</font></span>)</span> holds <br/>for <font color="Olive" title="b2">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( for <font color="Olive" title="b3">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> ) holds <br/>(  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )</span><br/>

<a NAME="E2:110"/><i><font color="Green" title="E96">A2</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="modelc_3.html#R8" title="MODELC_3:pred.8">is_homomorphism</a> <font color="Maroon" title="c1">v</font>,<font color="Maroon" title="c2">w</font>
 
<b>by </b><i><a class="txt" href="#E1:110"><i><font color="Green" title="E95">A1</font></i></a>, <a class="ref" href="modelc_3.html#T46" target="_self" title="MODELC_3:th.46">ThLTLNodes01</a></i>;<br/>
<a NAME="E3:110"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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="c1">v</font> &amp; not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> &amp; <font color="Maroon" title="c2">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="Olive" title="b1">x</font>,<font color="Maroon" title="c1">v</font></span>)</span> holds <br/>for <font color="Olive" title="b2">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( for <font color="Olive" title="b3">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> ) holds <br/>(  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">x</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="c1">v</font> &amp; not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> &amp; <font color="Maroon" title="c2">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="c5">x</font>,<font color="Maroon" title="c1">v</font></span>)</span> implies for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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" title="b1">k</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> ) holds <br/>(  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">k</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> ) )</span><br/>

<b>assume </b><a NAME="E1:110_1"/><i><font color="Green" title="E97">B1</font></i>: 
( <font color="Maroon" title="c5">x</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="c1">v</font> &amp; not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> &amp; <font color="Maroon" title="c2">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="c5">x</font>,<font color="Maroon" title="c1">v</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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" title="b1">k</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> ) holds <br/>(  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">k</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )</span><br/>

<a NAME="E2:110_1"/>
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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" title="b1">k</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> ) holds <br/>(  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">k</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="110_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">k</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> ) )</span><br/>

<b>assume </b><a NAME="E1:110_1_1"/><i><font color="Green" title="E98">C1</font></i>: 
for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</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"> (  <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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">k</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )</span><br/>

<b>set </b><font color="Maroon" title="c7">y</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>;<br/>
<a NAME="E2:110_1_1"/><i><font color="Green" title="E99">C3</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</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="c1">v</font>
 
<b>by </b><i><a class="txt" href="#E1:110_1"><i><font color="Green" title="E97">B1</font></i></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/>
<i><font color="Green" title="E100">C4</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k</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="c5">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font>
<b>by </b><i><a class="ref" href="funct_7.html#T73" title="FUNCT_7:th.73">FUNCT_7:73</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:110_1"><i><font color="Green" title="E97">B1</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
;<br/>
<a NAME="E4:110_1_1"/>
( 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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="#E1:110_1_1"><i><font color="Green" title="E98">C1</font></i></a>, <a class="txt" href="#E2:110"><i><font color="Green" title="E96">A2</font></i></a>, <a class="txt" href="#E1:110_1"><i><font color="Green" title="E97">B1</font></i></a>, <a class="ref" href="modelc_3.html#T47" target="_self" title="MODELC_3:th.47">ThLTLNodes02</a></i>;<br/>
<b>hence </b><a NAME="E5:110_1_1"/>
(  <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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">k</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c6">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E1:110"><i><font color="Green" title="E95">A1</font></i></a>, <a class="ref" href="modelc_3.html#D32" target="_self" title="MODELC_3:def.32">defSuccHom</a>, <a class="txt" href="#E2:110_1_1"><i><font color="Green" title="E99">C3</font></i></a>, <a class="txt" href="#E3:110_1_1"><i><font color="Green" title="E100">C4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:110_1"/>
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( 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" title="b1">k</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> ) holds <br/>(  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">k</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="c5">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:110"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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="c1">v</font> &amp; not  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> &amp; <font color="Maroon" title="c2">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="Olive" title="b1">x</font>,<font color="Maroon" title="c1">v</font></span>)</span> holds <br/>for <font color="Olive" title="b2">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st ( for <font color="Olive" title="b3">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b3">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> ) holds <br/>(  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font> &amp; <font color="Maroon" title="c2">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"><font color="Maroon" title="c4">f</font> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Olive" title="b2">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<font color="Maroon" title="c1">v</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
